Elves and other races have hundreds of years to get good at what they do — is the expectation that NPCs of these races would mostly be of high level?
How do I build a campaign setting that makes sense when elves live hundreds of years and should be mostly high-level characters?
The current answers try to patch the existing setting in order to make sense out of this broken and unexplained stereotype: the elves live much longer than humans.
If you want to fix the level inbalance problem, the best approach you can take is just to scrap the silly "the elves live longer" rule, assume they live more or less as much as the humans, and the problem is solved.
If something doesn't make sense, don't patch it: fix it at its core.
If you try to create a complex explaination to explain something incredibly senseless, you'll likely end up with many more broken things elsewhere. Don't dodge the problem, solve it instead!
Please notice I'm not claiming it's senseless that the elves live longer than humans; it's (obviously) senseless that if they live much longer they are supposed to be on-par with them, instead of incredibly more powerful.
Let me start by saying that this is a well-known potential "fallacy" in the settings/rule interaction
Human Level 1 Fighter: "Let me get this straight. You're a hundred and twenty."
Elf Level 1 Fighter: "Right."
Human Level 1 Fighter: "And I'm sixteen."
Elf Level 1 Fighter: "Right?"
Human Level 1 Fighter: "And we're equally skilled even though you've been at this a hundred years longer than me."
Elf Level 1 Fighter: "What's your point?"
Human Level 1 Fighter: "Are you an idiot?"
There are many possible ways to deal with this in your campaign, without requiring the participants to ignore it and "deal with it".
Previous editions like 3.5 did provide an indication on when certain races usually achieve their 1st class level, the age for elves being well over 100 years, unlike humans for whom it sometimes was less than 18. 5e has nothing like that in the PHB and, frankly, there is nothing preventing you as DM from doing whatever makes sense to. For instance you could say that an adult elf of over a century of age is, indeed, a rather high level NPC and regular level 1 elves are often no older than 30-40 years old, much like humans.
To be honest I had my first RPG steps with 3.5 and I do enjoy maintaining that age guideline it promoted. My personal way and suggestion of dealing with this is to assume that elves and other long-living races simply take a lot of time to patiently learn their art. When you have over 700 centuries ahead of you, it makes sense for you to want to enjoy your "teenage" years as an elf and learn at a much more relaxed pace. One should remind himself that Elves have Chaotic alignment tendencies meaning that they are not usually ones to demonstrate a lot of personal discipline self-restraint.
I usually imagine an elf's years much like Eragon's training [spoilers], who was a human, in the Alagaesia books, under the tutelage of an elven Dragonrider. Other than the core skills that he expected there was the demand to learn art, poetry, politics, historical facts. Things the elves believed gave them the wisdom and broad knowledge required to take decisions in applying their talents, a notion very close to the typical "elven wisdom" we see in D&D settings.
Eragon would often grow impatient, being used to the pace that humans have, knowing what a precious rare commodity their time is, a concept which elves might not grasp until much later in their life. In the book the rider would regularly mention just how much he despised this training and how much he wished they had more time to train him properly.
In overall, this is the attitude of the Elven race: to learn thing slowly and properly, never forcing one-dimensional knowledge and information upon someone, just like the way trees grow in nature. I believe this would explain why a 120-year-old elf often has the same level of knowledge and skills, yet a greater wisdom and experience on how to use them.
Alongside the above proposal, it would be even acceptable for a world to have elves that do take their first class level in a much younger age. Sometimes an elf flees his homeland, or simply follows it's own path in life. Such individuals might have been treated as youngsters and such behave in a typical rebellious teenager way, failing to demonstrate the maturity and wisdom their people are known for, yet having all the functional skills to live and survive, pretty much like a human of their age would have.
All in all, only the DM knows what's best for his group and his vision of the world, and would be nice to share that vision with the other players while introducing them to his, possibly, homebrew setting.
Elves don't get their first character level until age 120. That means they spend a lot of time until then doing... well... something.
If we look at humans and what they learn in their first 15 or so years, we can come to quite a range of different subjects.
As toddlers, we learn to communicate. This takes quite a few years to do proficiently. Making yourself understandable to your parents is one thing, but talking to other people is quite complicated, and that's on simple topics.
Then at some point we learn actual social interaction with others; not just words, but form and etiquette. How to address people how to bring up subjects, what is acceptable to talk about and what isn't, etc.
When we go to school, we learn the basics of writing, mathematics, history, art, science, our culture, and many other things. Plenty of people learn to write in cursive for who knows what reason, learn to play some kind of instrument, learn painting, maths, algebra, the history of their own nation, other nations, the world, about great people of the past, get some knowledge about basic science and the stuff the world is built out of.
Then after that, we specialize, learning either a profession or maybe to become a researcher which requires indepth study of a very narrow topic. After that, we're ready to explore the carreer world and start doing our professional thing. Or, slightly before we reach that point, we decide "sod it, give me a sword and something to stab."
Now... pull that whole thing into the realm of Elves; creatures of immense grace, almost limitless lifespans, with a culture and history to rival any other. After the first decade or so, your Elf child (they grow a bit slower, after all) reaches their true "toddler stage". They know how to do basic communication, they'd probably be able to pass as a young human, and if they learned their early communication in Common they might be as proficient as a human of that age.
But they're not learning Common, they're learning Elven. And being able to talk to a Human simply will not do. After learning basic communication it's time to be drilled in proper Elven etiquette. They'll need to learn to speak with that unmatched Elven grace and beauty that seems to come so easy to them, because Elves don't usually tell Humans that it takes them 30 years to speak like that. Humans wouldn't understand anyway.
(You know why Elves are always so aloof and arrogant to you? Because you are pissing all over their established etiquette. But they sort of accept that because you don't live long enough to learn it, anyway.)
So now our Elven "child" is already into their early 30s or 40s. They can talk like a true Elf. If you put them in a Human community (and teach them Common, but that's a vulgar tongue, so you don't) they would speak in words like a diplomat but have the wordly understanding of a child. Lots of words, but no substance.
To fix that, it's time for basic education. If you are looking forward to living to 500 and you have a reputation to uphold (remember that the Elven arts are the best there are, always), then this is going to take a while. Not only that, but whenever you learn about a famous Elf (there are plenty) you have hundreds years of history to learn. And your nation probably spans thousands of years, and with the life spans of those involved you probably have really good records of most of it, so there's loads and loads of information to learn.
Then you have art. Learning how to read notes and play the flute is, of course, not worthy of an Elf. Basic education involves learning to play the flute, harp, lute, violin, piano, drums, as well as voice. And proper drilling, too. You need to play each of them excellently. Of course this is all traditional Elven music... it's longwinded and requires patience to listen to; songs taking 30 minutes are no exception. Dreadfully boring to a non-Elven audience and mundane to an Elven audience, so while you can play all these instruments, those crude humans won't appreciate the sheer beauty of your perfected Harmonious Symphony and any Elves you meet can play it just as well as you can.
Then of course, other than instruments you'll also learn to paint, sculpt, write stories and four other disciplines of your choice. Again, all of these are traditional Elven arts (there are a lot of them) which aren't very interesting to other races, but they belong in a proper Elven upbringing. Some of them might even involve works of art that take over a hundred years to fully appreciate. While Humans perform crude arts like making bouquets of flowers, Elves learn to till a garden to perform beautiful flower art on their own, with no interference. As long as you're willing to wait a few years for them to grow, anyway. It doesn't really catch on with most races.
And finally, there's magic and science. After all, an Elf needs to understand both the history of magic, the theory of magic, and the broad applications of magic. Nobody ever tells you that 95% of magic isn't made for combat and adventuring, of course. After learning at the very least a bunch of simple spells and the theory of magic itself, Elves can probably hold an hour-long boring lecture on the theoretical applications of abjuration auras for the purposes of growing stone that lets itself be sculpted more easily than any human expert in that field. If there were any. There aren't, for obvious reasons.
So now that we've had another 50-60 years of basic education, we're approaching a hundred years of age and we have an Elf creature that has more experience than any Human will collect in their life! It's just all fairly pointless outside of Elven society, but then most Elves don't actually leave Elven society so obviously they're being trained to fullfill their role inside of it. The only thing that is left is to train for their assigned profession (perhaps another 50 years of smithing various pieces of jewellery, or maybe another 100 years or so to learn to play a chosen instrument even better, or maybe just more about the lifecycles of various plants so they can learn to plant a field of grain without disturbing a single creature, or another such Elven profession.)
Or they might learn the history and creed of their deity and set their first steps into Divine magic and go out to help the world. Or perhaps they'll learn some utility or combat magic and prepare a quest to recover some forgotten tome of knowledge. Or they'll learn to wield all sorts of weapons and armor and sign up for military duty. Of course they'll approach with that same Elven dedication as any other task and learn all of the involved theory, history, form and everything involved with their future task.
And then, around 120 years of age, they are ready to set out to bring glory to the Elves in the outside world. To an ordinary Human, they seem woefully underprepared for someone their age, but then the Humans don't appreciate the Elves' enyclopedic knowledge (of non-adventuring knowledge), their grace and understanding of language (mostly lost on said Humans, especially when speaking in the crude Common tongue, which takes them days to learn at worst), their theoretic understanding of magic ("just shut down the trap, we don't need another lecture") or their ability to play a host of instruments ("this marching tune takes how long? Don't you have anything shorter?") or all sorts of art ("whaddaya mean it'll take you 6 months to paint me? why on earth would you wait for each individual brush stroke to dry before you make the next?").
Now of course, it would be perfectly feasible to take a young Elf (say, 15 or so), give him a sword, drill him in the ways of combat for 20 years, and then use him as a reasonably trained soldier. Other Elves will consider that child abuse, obviously, so you won't get away with it for very long. Maybe if humans raised it like that, but then you're looking at what (to any other Elf) is basically a pointy-eared Human, culturally. If they ever find a 40 year old Elf who is travelling the country with a band of Humans and getting his adventuring on, he's going to be apprehended, disarmed, and sent back to school where he belongs. And the Humans will (at the least) get a very stern talking to about abusing a child like that.
(Sorry for the length of this, I got carried away!)
Probably the only "true" answer here is that it's handwaved because the rules are there to create a game that makes sense for the players, but that's not a very fun answer. So... ...elves stay among other elves well into their second century and don't go out adventuring; in fact, like humans, many never go adventuring, so even elves nearing their 700-year lifespan are still likely to be non-leveled NPCs. ...going hand-in-hand with this, elves are frankly not all that interested in the affairs of lesser beings. While they might live up to 700 years, few if any spend longer than 70-80 years out among humans and the rest of the lot before returning to the communities that birthed them. ...adventuring elves are no more likely than adventuring humans to meet a non-violent end, so don't expect to live for a millennium when you spend the bulk of your time digging in monster-ridden holes for treasure.
My setting has some combination of all of these; the younger elves venture out to gather wisdom and knowledge about the world; once they have learned all there is to know (a handy in-game euphemism for reaching 20th level), they are to return home and enter a new phase of their life, wherein they will no longer interact with the outside world or even the younger elves. In this second stage, they study and contemplate all they have learned, in preparation for an eventual chrysalis into the feywild, where they will take their place among the archfey.
...but yeah, all of that is just me justifying the handwavium.
An excellent resource for you to consider:
This is fan-work, not official, but it is written by a fan with a deep knowledge of the setting of D&D. It provides a very interesting look into elven society and personality, and the concept of long time goes a long way towards explaining why elves take so long doing things.
Basically, that famed elven grace and fluidity doesn’t just happen, you need to practice at it. A lot. Being that graceful means perfecting every movement, making every movement of every action as beautiful as possible. And elves enjoy doing this immensely, and find the frenetic hurry of other races extremely irritating – but, of course, they are capable of hurry, if they need to, and of course adventuring elves have to put up with this irritation more than most.
Humans live longer today than they did in the (relatively recent) past, but they're less well prepared for life until later in life than they were back then. Medieval folks would already be training for their adult occupation by the time they were 12-15 years-old. These days, they're considered children, and barely trusted to walk to their friends' houses, much less spend a few hours in the local park while mom & dad are at work. If you spend decades culturally being viewed as a 'child', why would that give you an advantage over another race who only spends 10-15 years in that stage?
My answer will draw from other answers, but give a reason why based on stats.
Elves of every type take longer to learn things in order to learn them proficiently by their own standards. This can be evidenced by the stat modifiers that elves have, while not attributing them to anything outside the range of their stats. Apply the stat modifiers to a long-lived race and you can reasonably come to the following conclusion:
All elves have +2 Dexterity. This translates to meaning that they have taken the redundant practice of all of their tasks to perfect the motion of these actions. If they are trained in art, then they are simply more precise with their brush strokes. If they are trained with swords, they are more accurate and artistic in their strokes of the blade. Their movements are intentional and precise, sure-footed to the smallest degree (compared to other races).
In addition, elves have very good vision. they see the smallest details and the most minor flaws in objects. Anything outside of perfection in the applications of their skills would be barbaric. A wrinkle in the fabric of a piece of clothing they made would be an unacceptable disgrace to their beauty and skill. With their perception and their natural grace and dexterity, elves overall take the time to truly perfect their precision at any task they perform.
This precision and attention to detail means they are almost insulted by things that aren't precise. We can assume that not only is the elven language melodic, but inflection is likely as important as word and they are likely to have even more subtleties in these inflections than any other race. Think of the difference between normal speech, incredulity, and sarcasm, and make the differences between them so subtle that most races would be unlikely to even notice a difference in speech patterns.
How does is this impacted by specific races of elves?
High elves are the easiest to address in this context. They must know everything possible in regards to any topic of study and have a broad range of skills. They are exceedingly intelligent, meaning they generally know more than the average member of any other race about anything they know about, and in fact, everything they have ever known. They know this for a fact. It's pushed in to them. A high elf considers others beneath them because things that they consider standard knowledge of all high elves are considered skilled knowledge to other races.
Wood elves are extremely perceptive and intuitive (high wisdom). They would be learning not simply to see things better in the sense that all elves do, but to see things in the way they connect to each other. They see abstractions and metaphors in every day actions and happenstances of nature. Other humanoid's actions would be simple things for them to read (intuition), and they would consider the other races barbaric for their lack of empathy. They would likely consider non-elves to be naive (because other races don't see things as easily as they do). This is likely going to create feelings of superiority among the wood elves because they appreciate life far more than most races, and are quick to observe the motives of others, even in subtle things a such as a metaphor about a corrupt king hidden under draconic designs etched into a longbow that an elven ally had crafted.
Following this same path, for the Drow everything they do is a manipulation, and their century of life represents this. Everything is about getting others to do as they want. They fight against their own kind in this competition on a regular basis... against those who are already skilled. A piece of art that they have painstakingly create is intentionally designed to spark specific emotions, and thus make a creature more susceptible to other control methods like overt orders or subtle influence designed to create more followers. They lie, cajole, manipulate, and pretend, exerting their force of personality on each other in a myriad of different ways.
Everything a Dark Elf does is an attempt to manipulate others, and the degree of this that they have is something that raw strength alone cannot touch. This is made even more pronounced by their perception and finesse because their intent is easy to hide, but still effective at producing the desired reaction out of others. They consider others beneath them because they cannot see the Drow's intent, and they cannot hide their motives as well. The only exception to that is Wood Elves, who the Drow would know full well can spot their ruses, and the High Elves, who can investigate to find the root of their machinations. They are trained by their own society that manipulation is a necessary form of survival, so in training to use tools, they must perfect application in all forms, from the precision of the strike, to the place to stick them to make them scream just right. This is bred into every aspect of what they learn by their society, from art, to fighting/torture, to playing the political game that is ever so present in R.A. Salvatore's work. If you get caught in your schemes, you are punished. If you get away with your attempts, it is its own reward because you gain what you were trying to get.
Patience
As Elves are all long-lived, they are also a very patient race. They move at a pace that states that in all the things they are trained in, they are able to take the time to do it right. If there is never a reason to rush, why would you? It isn't like you are going to die for another 500 years. Take the time, do it right, and perfect and hone your craft.
How does this relate to their 'initial level'?
It is only the most extreme circumstances that causes someone to actually become an adventurer, especially in a society where patience is appreciated. Character levels generally come from meeting extremely dangerous situations and overcoming pressing problems in a way that elves are simply unused to.
They train for decades to become first level warriors/mages/etc. because they have all the time in the world, and they want to master their skill. This is not the same as actual combat experience, however, and they have not become inured to the experience that physical danger truly brings. When they are put to the fire, they begin learning at the pace of everyone else (much to their own likely annoyance), and one of the first lessons they are likely to learn is that sometimes patience is not as much of a virtue as they generally believed.
Summation (TL;DR):
Their years don't teach them to simply perform their tasks, it teaches them to perform them with precision and skill based on the focus of that sub-race. These foci are a part of their very being in all aspects of their training and everything they are taught is influenced by this and considered important to their training because of this. They don't simply learn their skills, they master the subtleties of it. Only extreme circumstances cause them to move at a faster pace and gain experience as an adventurer would.
Your question assumes that all elves are already hundreds of years old. Just as all humans on earth are not 75, all elves in a Dungeons and Dragons campaign are not on their deathbeds with many tales to tell of adventures long finished.
Additionally, there may be cultural influences in your world where elves and dwarves are not allowed, not encouraged, or not interested in striking out on an adventure that very well may claim their life until they are 120 years old, and thus have only theoretical and no practical knowledge until they reach this age.
As others have said - if you live 1000 years, you think about the long game, whereas humans know their time is short. Humans prep, train and take on all they can in their (relatively) short little lives. They must strike down injustice as soon as it crops up--they don't have time to wait. Elves can simply outwait evil, provided its cause is not also very long lived, therefore the perceived need for such skills in elf society would likely be much lower.
The only elves in the Monster Manual are drow. Even "lowly" Drow (p. 128)are far more capable than human Commoners. The other drow are among the most capable humanoids in the book, with challenge ratings 5-8.
Not every member of the city watch, the village militia, or the queen's army is a fighter. (p. 70)
Adventurer's are special cases, the most capable people in any population. The stat blocks for NPC's in the back of the Monster Manual back this up - neither a Bandit or a Guard have all the capabilities of even a second level fighter.
Take a look around your school or office building next time you get a chance. How many people that you see are good at...anything? If you just breeze through life, you never make it to (ahem) the next level.
One of the pillars of D&D is that a when someone "goes on adventures and overcomes challenges" (PH, Beyond 1st Level, p. 15) they become more capable. These adventures include combat (PH p. 8). People, 200 year old elves included, who don't seek out danger have to improve themselves the slow way, if at all.
Consider Bilbo Baggins - he was 50 years old when he set off on his first adventure. He was good at the things every hobbit was good at, like moving quietly, but really not much good in a fight. A few brushes-with-death later, and he's taking on whole colonies of spiders.
Speaking of Middle Earth...
One of the many inspirations listed in the DMG (1st edition and 5th) is The Lord of the Rings. (Mind you, I'm referring to the books.) In The Lord of the Rings, many elves were among the wisest, most powerful creatures were elves.
If this makes sense for your campaign, let elite elves all be high level.
Oh, I remember being curious of that when I first met Formentera. I was 15 and he was like 100 something. Sure he looked a lot more confident than I was, and carried himself with an elegance and he was such an excellent archer, but I would have thought a century on this world would have turned him into a fighting machine. I thought about asking what in the world he had been doing all those years, but I felt that would be rude - really rude particularly because he carried himself in such an otherworldly manner.
Over time as we adventured together, I came to partially understand (grok) what was so different about him. You see, elves do everything as if they are like hobbies... Let me give an example: I love writing, I spend so much time telling stories like this, but I would never take up writing as a profession. I like dancing, just ring a doorbell and I could start moving my body, but I would not consider earning my life as a professional dancer. Now, people eventually pick one profession or another, right? Well, no, elves don't. They do everything as a hobby, they do not feel the same urge to excel in one thing and fill their life with it. It is like they are in a perpetual holiday, they wake up with the dawn, they spend time in nature, they sing songs, write poems, dance, or even just sit down and contemplate about life, the multiverse and everything. Why do you think they are not easily "charmed": all that philosophy makes you reach an inner peace, you can not easily influence such a mind. Why do you think they do not need sleep: all that meditation binds your mind and body into one.
Just think about it. When you have centuries in front of you and a chance to experience life as it is, without the worries of earning your livelihood, supporting your family, raising kids, without the need to prove yourself to anybody, how would you behave? It is hard to imagine, because you think even the best holiday might eventually become boring, huh? Now imagine that watching the dawn every single morning never becomes boring as you perceive slightly different things every time. One time you hear a new bird chirping, another time you see a slightly different color in the clouds, and most importantly you understand that you have changed a slight bit so the whole multiverse is different for today's dawn than yesterday's. A perpetual summer vacation that never becomes boring. Ok, now tell me, would you care to become super efficient with your sword or spell today? Or would you leave it to another day, perhaps in your third century if ever?
Very rarely, they become adventurers. And once they get into the business they sure excel the same way as other races do. But even when adventuring they see the world differently; to us they appear aloof. I imagine to them we look impatient, we lack a real purpose, as we can never see the big picture the way they do. But much like they care about all the plants and animals, they care about us too and stay with us and make friends. Stay with them for a while and let them nurture your soul.
Statistically speaking adventurers of any race have short careers because they live exceedingly risky lives battling hordes of goblins and orcs, all manner of supernatural creatures, the undead, mind boggling horrors, and even the occasional flamethrower-toting dragon. As a result many adventurers are killed before they have the chance to live very long and garner much experience.
An elven adventurer who had spent a hundred odd years adventuring would indeed be mightily powerful. However such an elf would also be very, very unlikely to have survived those years and thus a very rare encounter if even possible at all.
A potential Elven adventurer who has spent a hundred odd years perfecting his skills without any risk would not be anything like as dangerous an opponent.
As the game rules reward only the taking of risk with experience and levels we can conclude that our 120 year old 1st level Elf character must be one who has not taken any risks up to this point.
There's no mechanism in the game for rewarding endlessly practicing your skills only for using them 'in anger' but we can assume (as the other answers have pointed out) that the Elven stat bonuses to Dex and Int (or Wis) are the direct result of that hundred years of study and practice.
That practice can take a low level Elf's skills beyond the maximum human possibility as a 20 Dex Elven archer will always be better than the most dextrous Human, a 20 Int Elven Wizard will always know more spells than the smartest Human Wizard, and a 20 Wis Elven Cleric will always have a deeper connection to their deity than the wisest Human. Contrarily Elven and Human Sorcerers, who rely on force of personality to power their magics rather than extended practice will be on a similar footing.
So to think that an older character must be more powerful/higher level than a younger one, simply by virtue of being older, is thus a mistake, albeit one that is easily made. In the D&D setting it is the taking of risk that makes a character more powerful, not the effect of aging.
This question has a lot of excellent answers, but even with all of the answers there is one thing I think has not been directly stated by anyone else.
In the real world, among humans, years of experience means little. Note I didn't say nothing. Someone with one year of experience almost certainly knows more than someone with none, and people will tend to improve over time so experience does matter.
But, it is very possible to get into a settled routine and improve very little after you have achieved minimal competence in the core skills necessary. Just repeating what you have already gained competence in does not help you get better. You see this in the real world all the time, but it is obvious with programmers. There are virtuosos who work on challenging tasks and study to keep up with the latest technology and learn new techniques. They develop quickly and can be very impressive very soon. Then there are those who learn enough to perform their basic task and do it repeatedly and they grow very little. You especially see this with people whose only job is to maintain and tweak legacy software that was put into place years ago. I was a software engineer for a time and I had friends fitting on both ends of that spectrum.
Also, I am very bad at Go. I've been playing for more than 20 years, I started in college and never stopped. But I don't study it, I only play. I don't even play consistently or with maximum effort. It is a game I play recreationally now and then. There are plenty of people that aren't even 20 years old that are much better at Go then me even though I've been playing longer than they have been alive.
If this happens with humans, you can assume it would be even more common with elves with enormously long lifespans. The elves may always assume they have more time to study later. In fact if anything they might have it worse because they could easily get stuck in well developed ruts and then resist changing the techniques that they have been accustomed to using for longer than a human has been alive.
It is therefore perfectly reasonable for a human to be as or even more skilled than an elf if the human puts in more effort and goes out their comfort zone.
If you want to argue that an elven adventurer would surely put in a lot of effort to becoming good at their skills because their life might depend on it, I assure you that isn't necessarily true either. I served in the Army for a time. Even when we knew there was a deployment coming up, there were plenty of soldiers that put in the bare minimum effort to avoid being disciplined. Don't get me wrong, I served with some absolutely amazing soldiers who went above and beyond and even those who did the minimum were my brothers and sisters. But...I can attest there were plenty of them that did not put a lot of effort into their training even when they knew they were heading to a war zone where their fitness and skills might affect whether they survived.
I won't belabor long-time or the fact adventurers are special since other answers have covered those two explanations (and more) better than I could.
But long-time is worth emphasizing because it dovetails with my argument that years of experience means little. In the real world it means little for humans and for anyone that might experience long portions of their lives as long-time it means even less. As noted in the answers that discuss it in more detail, I am not aware of anything official that states DnD elves live in long-time, but it fits very, very well with the official lore that I am aware of.
I would also not underestimate the significance of the fact that adventurers are special. Even if we assume for the sake of argument that the average elf is much more skilled than the average human due to their longer lives, that might mean absolutely nothing when it comes to discussing adventurers who are explicitly exceptional as discussed in the players handbook.
Speaking as a D&D newbie (so my thinking is as much inspired by Tolkien as D&D):
The core issue here is that two starting characters with very different ages have similar skillsets/levels.
Some answers I see here focus on producing a reasonable explanation as to why the age difference would not provide an Elf an advantage. I still think this is fundamentally flawed.
For example, it may be reasonable to say that your Elf is a level 1 warrior at age 120 because he spent his life as an academic, locked in an ivory tower. Now, at 120, he's just picked up the sword. The problem I see with this, however, is that none of the Elf's other stats that would be related to his past (in this example wisdom, intelligence, other non-martial skills) will have any significant advantage over a new human player.
My general argument is that
My suggested solution for this issue would be a fundamental change to the balancing between the different races. I think elves should be balanced in such a way that they actually do have significant advantages over humans due to their increased life span - in other words, make the age of your character a factor in determining the levels of your skills, and come up with reasonable disadvantages for balance.
"But smohyee, what 'reasonable disadvantages' could you really give an elf?", I hear you asking in that irritating tone. Well, that may be a good point (others know elf lore better to judge). But insofar as it is a good point, what it suggests is that the lore itself is unbalanced. For gameplay's sake, we want our human character to be roughly equal in starting advantage to an elf character. But all the lore/stories I've encountered make it pretty clear that elves are awesome generally superior to humans in many ways.
TL;DR: Elves with an age advantage should have a skill advantage, because that's how life works and because game and other lore portray Elves as naturally advantaged/superior
This question makes some base assumptions that have nothing to do with specifically elves but are in fact quite general
Why would an old character be low level? The actual age here isn't relevant.
Asking why a 200 year old elf is a level 1 fighter same as a 15 year old human is same as asking why a 60 year old human is a level 1 fighter same as a 15 year old human
The answer is clearly : because they started being a fighter recently.
The elvish fighter who is 400 year old and yet level 1 doesn't translate to them being a fighter for 300 years, same way a 60 year old human being level 1 fighter doesn't translate to them being a fighter for 45 years. Their low level is a reflection of the fact that they became a fighter recently
Now an important fact here is that none of this means they were not involved in military in the past. They just never pursued a class
Npcs often have stat blocks that do not level up. That translates to a person who lives their life doing one particular thing as a job for example, but neither dedicates themselves to improving nor focuses all their life to it.
A random guard for example goes to work in the morning, guards the gate, and then goes home to her family. They don't train to become better or actively try to achieve something other than fulfill their duty. For a real life example, consider a person who knows how to do a job but are not particularly interested in progressing in the field or honing their skills. Most people operate like this in fact.
Classes on the other hand are defined by their ability and dedication to improving, aka xp and also have the chance to experience new things and apply their skills constantly. Consider the guard again. They neither train further nor face foes every day, but instead sit at their post and be a guard. The average fighter on the other hand spits in the eye of death on the daily.
So what does all this lead us? Firstly characters are assumed to simply not had a chance to level up or have a class before they gain their first level. This is explicitly the background system.
As for elves, the way the system deals with classes and experience tells us that most elves would simply operate the same as anyone else, just for longer. A human is a guard for 40 years and then gets a pension, an elf for 500.
The only think specific to long lived races here is that this kind of scale would also mean that there would be some individuals who have devoted their lives to self perfection and would ,from an in universe perspective, have achieved a tremendous mastery over their field( of course this is a process that is tremendously slow as you hit a point of diminishing returns sooner or later. Imagine that an elf might take 100 years to achieve the transition between level 19 and 20 and so on and so forth, especially when doing so through training instead of putting themselves in life and death scenarios).
But in general, this is how elves (and other long lived people) are already portrayed in most dnd fiction and worldbuilding which is evident if you study lore and books that deal with the topic
In addition something like this would usually be restricted to npcs. This is often the case in adventures. For example the final boss of tomb of annihilation, acererak, a particularly long lived lich even by liches standards, has extra abilities and such due to his mastery his age and dedication has given him, on top of the lich statblock.
Based on all of this, the only people who would truly have a significant difference due to the scale of their lifespan would be those few who devote that lifespan to seeking self perfection, and would thus have a leg up over similar kind of creatures, npcs, or monsters.
From a gameplay perspective if you want to apply this to npcs with stat blocks consider giving them one or two extra abilities, and for npcs with class levels, increasing relevant ability scores by 2 or an epic boon
Why should Elves all be high level characters? In addition to what others have said about taking time to learn Elven culture, why bother learning human things? If you know you're going to live effectively forever barring something terrible happening, why not wait until tomorrow? There's no sense of urgency toward doing anything. Further, for creatures who'd live forever without violent/accidental death, the drive to avoid the opportunity for such a death would be much higher. A human might be willing to sacrifice their life, they only had another 20 to live anyway. But as an Elf, is it worth dying when there's another thousand years or more to live?
"How do I build a campaign setting that makes sense when elves live hundreds of years and should be mostly high-level characters?"
Are you talking about players or NPCs? If you're talking about players, then you may need to tell them to change their backstory. A 200-year-old elf that's a veteran of a dozen wars wouldn't be clearing the Inn's basement of rats like a level 1 fighter looking to pay his tab, and he wouldn't become several times better at fighting during a single adventure. Maybe the 200-year-old elf came from a peaceful village and returned from a hunting trip to see that it has been destroyed and so picked up a sword for the first time in his life?
As for NPCs, well there is such a thing as natural talent. They shouldn't be gaining levels during play. Maybe those elven guards have never actually had to fight or go on adventures to get better at their craft?
I think the problem though is that you are trying to make the world "make sense", but only in relation to the rules of the game. The rules are there to support the adventure and shouldn't be the focus. If you are designing a campaign for level 1 characters that are supposed to defeat experienced 200 year old elven veterans then you might need to rethink your campaign.
