Per AlienAtSystem's answer, I've decided to tell you about my experience with trying to streamline leveling.
I was asked by a local gaming convention to set up a non-AL group game as part of their "Intro to Tabletop Roleplaying" experience. I went way overboard, writing up a 4-hour mini-campaign inspired by Nightmare Keep that I called "The Heart of Wolover." The entire adventure took place inside a dungeon/animated corpse, with rooms themed around body parts, and the goal was to give each of the five parties experience with the major aspects of D&D in the course of a single session- role-playing, obviously, and NPC interaction, group and individual combat, puzzle solving and trap disarming, and climaxing with the surviving parties ganging up on a hydra variant "Heart Wyrm" in the four-chambered, still beating heart.
- A word of advice- never do this. The project took nearly 80 hours to
put together, all for a single afternoon session. I am certainly
never doing it again.
Anyway, the important bit is that I wanted the parties to gain their first couple of levels rapidly, so the players could see and appreciate the difference between their characters at 1st level and those same characters at 5th. My previous experience with leveling parties indicated to me that, under normal circumstances, the players would have spent most of the session leveling up, especially since they were new to the game. I therefore needed a way to make leveling as fast as possible for a large group of people.
I used a stack of pre-written leveling notes. A rogue, for example, would receive a note when they hit level 2 that read something like,
Congrats, you've hit level 2! You gain the following:
5 hit points (plus your Con modifier)!
You can now use a bonus action on your turn to either Dash (move your speed), Disengage (avoid attacks of opportunity) or Dodge (gain advantage on Dexterity saves and give attacks against you disadvantage)!
Leveling up this way meant that the vast majority of the legwork was pre-done for the players, and with the notes handy, they didn't need to write down new class features. They still had to track hit point gain, but I used the average recommended by the PHB instead of having them roll. For a level gain that featured archetype selection, my little note included a line like, "plus, PICK ONE of the following features..."
For spellcasters, rather than give them a full list of spells to pick from, I assumed they would always pick the highest-level spells they could, so for example the wizard instructions for levels 3 and 4 read, "Pick two new spells to learn! You can choose from the following:" followed by the 2nd level spell list.
How did it go?
So. Much. Paperwork. Did I mention I'm never doing this again?
The bright side is that average leveling time was somewhere around five minutes apiece.
Wizards took longest to level, and if I did try this exact setup
again, I'd have a table of spells to consult that looks a bit like
the spell lists from d20pfsrd.com, which helpfully includes a
one-line description of each spell.
Writing out notes for the different archetypes took the longest, although I only had to worry about one set of archetype features per class- if you're looking to advance to 20th quickly, you'll have to worry about that more. I had no complaints from the players, who were either new to the game or new to 5th edition, and only mild grumbling from the half-dozen DM's I wrangled for the session about the extra paper they had to track and hand out.
The biggest source of complaints was myself; while in-game leveling was easy, it meant a lot of extra work for me in particular. It also meant that I had, roughly, 50 notes to hand out, with a copier on standby. With a smaller group of people and advance knowledge of what classes and archetypes they'd be, the amount of extra work would be cut drastically, but there would still be a lot extra work.
Pre-written leveling notes made leveling up faster and easier for the party. For the DM? Not so much. But you might find it's worth it.