First time I ever played the Sentinel Comics RPG using the original starter kit (not the new one that just dropped - this was pre-COVID) the GM bought it and had us playing a half hour later after he did a quick skim of the mechanics and the adventure he picked to run (it came with six). We used pre-gen characters, so no time spent on that. Pretty normal for better-made starter kits without complex game engines (eg Pendragon) IME, although the experience is probably better if the GM has actually read everything the day before.
If your GM is familiar with the system already the SCRPG core book would do the job just as well. It has pregen characters and a couple of starter adventures right in the book, but the full rules are about 32-40 pages and would take most GMs more than a half hour to digest on first read.
FIASCO is 100% pick up and play with a few minutes reading and explanation if no one's ever played it before. The very idea of prepping for it would feel weird. Same goes for Baron Munchausen unless you're going to declare it a non-RPG (which I wouldn't really argue strongly one way or the other).
Over the Edge could get you playing within a half hour including character gen and a real basic run-down of Al Amarja, although the GM would probably want to have everyone playing newly-arrived tourists rather than more in-the-know natives. The session's likely to be more about encountering and dealing with your first bits of weirdness than advancing personal schemes, but that's okay. I've had several good times just getting through the airport in past campaigns.
There's plenty of others if you allow the GM to be familiar with the system already. Explaining the basics and using published pregens or a simple chargen system can be a 10-30 minute process even with newbies. If the GM is just picking up the book for the first time then the game options are more restricted, but I don't generally consider "reading the rulebook" as session prep myself.
Yep.
Fiasco is one I was going to mention. No prep, just play. Classic pick-up game.
Over the Edge is another. Jonathan Tweet did a game like that at a con and taped it. It’s on YouTube.
Eat the Reich comes with a simple premise and pregen characters. You’re up and running in maybe five minutes. As well as its precursor, Havoc Brigade.
Paranoia is another. Players are not supposed to show knowledge of the rules, making it a classic black-box game. Character creation in XP is or can be random, there's an online character creator. All you do is hit "decant" and you have a random character to play. So inside five minutes you're up and playing.
DCC RPG and MCC RPG both have random character creation and an online generator. So you're playing inside five minutes.
Most one-page RPGs have minimal if any character creation, so you're playing in no time. Honey Heist, Lasers and Feelings, and any of the hundreds of hacks of those.
Minimalist RPGs like 2400 and its many hacks take a little longer as there's some character creation, but nothing like D&D 5E. Maybe ten minutes at the outside. While a little more involved, many OSR games are super quick at character creation, if they're not randomly generated. So games like Mork Borg, Pirate Borg, all the X Borgs, Weird North, Knave, Into the Odd, Black Sword Hack...on and on and on.
Captain's Log is a solo RPG by Modiphius for Star Trek Adventures. You don't need a group, just a spare few minutes and a desire to play. Mythic GM Emulator can turn any RPG into a solo RPG. Many other solo RPGs exist like Thousand Year Old Vampire and Colostle.
Any game with random character generation you can be playing in a few minutes.
Any game where the players trust the referee to run the rules you can be playing in a few minutes.
Any game where the referee either procedurally generates content or improvises content you can be playing in a few minutes.