I’m thinking games like Exploding Kittens or Fluxx. Neither requires lots of explanation and is easy to set up. For Fluxx it is even possible to join in the middle of a round, just grab three cards and look at the current rules.
Another option is The Crew, if you limit yourself to simple missions.
The Crew includes a log book where you track you progress in increasingly more complicated setups. We have played it through once for The Crew: Mission Deep Sea, but mostly we just ignore it and start at a reasonable difficulty level and increases the level once every time we win the game within a session.