Disclaimer: I am writing a different answer because I believe this answer goes on the completely opposite way of my original answer. The reason for this new answer is a bounty asking explicitly for answers that are not frame challenges. I still believe my original answer is the best I can give to the original asker problem and to most DMs having this problem, especially if they are new (as in the case of the question). I believe the answer below is a good solution if you are hard on the restraint of 1st level.
Furthermore, I will challenge the frame posed from the bounty itself before I answer it properly: If you are running a one shot, I strongly recommend that you start at least at 3rd level. In 5e, at 1st level, most classes don't even have their defining features or any combat options besides "I attack", and, maybe, sometimes, "I help my ally who deals more damage than me to attack (with advantage)". Take the Paladin as an example - the Paladin has 5 points of Lay on Hands, and, maybe somewhat useful, his Divine Sense. He does not get his Divine Smite, Spellcasting or Fighting Style until 2nd level. A 1st level paladin is a bad fighter with a holy cross in his shield.
This isn't even the problem when making a villain encounter, it is a problem through the whole session. In my experience, 1st level is great to build up characters for a long campaign and set a mood, but awful for stopping your play there. There is a reason you level so fast to 2nd level.
But now, what if you and your players really, really, really want to play a 1st level one shot?
Do not make the encounter about defeating The Villain
Through this answer, I will give an example we actually ran, although at 3rd level, while tackling on the problems specific to 1st level and how to handle them, and presenting the general idea behind it. The setup was the following: A bunch of evil Drow cultists were performing a sacrificial Ritual to Summon the Goddess Lolth into the Material Plane.
Among the villains performing the ritual, we had a Priestess which CR would probably be around 17 - certainly deadly to a 3rd level party.
The goal in this encounter is not, and can not be, defeating the Priestess. That is ultimately an impossible goal. A good encounter is a clash of motivations, goals, objectives. (See this angry DM article about it - Disclaimer: as usual for Angry DM, lots of "strong words"). In my example, the Priestess wants the Ritual to succeed, while the adventurers want to stop it. It is not a one-on-one combat, and victory or defeat are not defined by one side dying.
So, during the whole encounter, the Priestess is ultimately busy with the Ritual. If attacked, she would probably cast Shield and keep focusing on the Ritual. If she ever stopped to attack the party, the Ritual would fail and her lifelong plans would go to dust - meaning the party has obtained victory, maybe at the cost of their lives, but a small price to pay for world's salvation. In the specific case of a one shot, as long as the players are okay with it, the ultimate resolution may involve the characters' death, and can be satisfying, although perhaps bittersweet, to know that the characters were martyrs that saved the world. So, this is my first point: since it is a one shot, do not fear characters' death so much.
Extending this line of thought, defeat is an acceptable outcome. Defeat happens. While D&D is mostly built around the assumption that the characters will win, it is also built around the assumptions that they will level and grow. If you are willing to throw away one of these assumptions, you may as well throw the other.
Obviously, the Priestess was not alone on her cult, and certainly would not perform the ritual alone and without anyone to help against potential intruders. This is where the characters can get level-appropriate encounters: through the minions of the villain. Given the Drow thematic, we had Giant Spiders and, in the setting, Goblins are essentially Drow's slaves, so we had a bunch of goblinoids to kill as well.
While the motivation belongs to the villain, their minions are effectively the ones that are fighting the party in the clash of motivations. In the example, the minions had to bring body sacrifices to a table, and perform a bunch of stuff I would prefer not to describe here, while fighting the party. After some time, the party understood that a major structure in the room was required for the ritual, and attacking that structure would delay or even stop the ritual. The minions are the ones responsible for stopping the party from freely attacking the structure.
Just make sure the minions are an appropriate challenge to the party. Here enters the first problem of a 1st level party: an appropriate minion challenge is, still, a little underwhelming. The powerful priestess has, as her minions... Four goblins. But if you and your party can run with that, then go for it. Otherwise, you can improve the looks of it. Perhaps the priestess has an army of 50 goblins, but 48 of them are too busy helping with the ritual, they are too brainless to understand that the characters are a threat and they are more scared about stopping the ritual and being slaughtered by their Drow overlord than they are of the characters.
Make the environment part of the encounter
As I mentioned previously, in my example, the ritual structure was a major part of the encounter. This already provides a somewhat meaningful decision for the players: should they focus on the minions or on the structure? This is even more important for characters at 1st level. They have very few possible decisions to make within their own features and character, so your encounter must provide meaningful decisions for the players. A 11th Wizard can think for minutes on what spell it should cast, so his features by themselves provide that, but a 1st level has Magic Missile and Sleep, and probably he is spamming Fire Bolt because he only has 2 spell slots anyway.
One way to solve this problem is to make the environment meaningfully interactive. This is very common in video games, where the way to defeat an unreachable boss is through the environment. In my example, the environment is a proxy to the villain, i.e., it represents the HP of the encounter. You can also make the environment a tool, say, by inserting flammable barrels that will explode in a Fireball-like way when touched by fire (the fighter can do that, riskly, with a torch, or the wizard can do that safely with a fire bolt). It may, as well, be a defensive tool. In 5e, spells require line of sight to be cast, and you have full cover if there is no line of sight between you and the center of an AoE spell. Maybe the powerful Villains indicates his intent to cast a Fireball in the center of the room, but the party has enough time (and clues) to hide behind the pillars. Such mechanics are, again, very common in video games, and can be used to provide meaningful decisions to the encounter.
Important consideration: if the environment is the proxy for the HP of the encounter, make sure the players understand it. One of the major flaws in the encounter when we ran it was that the players took a long time to understand the structure was meaningful, and that attacking it had any effect. Describe how the minions are clearly trying to protect that structure, how the villain gets annoyed by the party hitting it, anyway, convey this information the best you can. Same thing for using the environment as a tool. Make sure it is clear to the players that the barrels and the pillars are useful, not just a flavorful part of the scenario description which can be forgotten.
There are many ways the encounter can end. As previously mentioned, maybe the characters die and the villain succeeds. Awww, it sucks - but can happen, especially in a one shot.
The other way is through the characters accomplishing their goal. But now what?? The Villain could, now, full of anger, just kill the characters, with their plans frustrated. Unlike my previous scenario, where the villain is forced to give up his goal in order to kill the characters (therefore, their deaths have meaning - it is what saved the world), now the death feels a lot more frustrating, because it seems meaningless. They already had completed their goal, if they die now, it is for nothing. Sure, you can rationalize that as a consequence of saving the world, but it does not feel good. What can you do?
Deus Ex Machina
I am getting about 5 downvotes for actually suggesting this, but a Deus Ex Machina is a literary tool and can be used. Even Tolkien has his Eagles. Some deus exes may even be well built enough that they do not feel like a deus ex machina. In my example, the deus ex machina was a powerful (allied) Wizard sensing the disruption of the ritual structure and teleporting the party out of there. If you want a more conclusive mean for the example, you could
Say that the priestess is extremely exhausted from performing the ritual and does not have the strength or spirit to defeat the party, being an easy kill.
Lolth herself, who was half-summoned, gets frustrated with her servant failure and punishes her with death, before being banished away back to her plane.
Just be creative and as coherent as you can. If the party already has the fulfilling emotion of having their goal accomplished, from my experience, they will not get too bothered with a small deus ex machina to avoid the characters downfall.
So, this is my 50 cents on encounter design for a 1st level party. It still is not a conventional encounter or villain1, but, from my experience and in my opinion, is an engaging encounter that will let everyone have fun, which is the main goal as far as I am concerned.
1 Final Final Comment: By the way, you may notice that the threat (an incredibly powerful priestess summoning a goddess to the world) is considerably above the pay grade of 1st level adventurers, reason I say this villain is not conventional. I do not care. Both the Hobbit and Lord of the Rings are about a bunch of nobodies with one or two magic items defeating ancient dragons, one or two ancestral godlike angels and an infinite army of evil creatures, and D&D is literally founded on the basis of Tolkien's works, so do not tell me 1st level adventurers should be restrained to a Thief in The Shire.