Science

Plus drunk people get up to some real silly shit they might not otherwise get up to and probably accidentally stumbled on some other advances.

I could see the wheel coming out of drunken escapades, probably starting with a game of "how far can roll rock down hill?", which led to shaping rocks to optimize their rolling distance, and then later attaching two rounded rocks to each other with a stick, then the realization that trying to stand on the stick and make it move is fun, then some people trying to put something on top of it that's easier to stand on and eventually finding a primitive bearing system that probably went through many sticks, which led to the invention of lubrication (which would have started as reinforcement with grasses until it was discovered that the oils from the grasses make a bigger difference than the grasses themselves), and then at some point someone pulled it around for their kids or something and then someone thought of having animals pull them. They probably had the first chariot races later that week and then Gilgamesh used them to conquer the known world because you could stick a lot of food in them and keep an army going for longer between raids.

Though it was probably logs that led to the wheel, since they can skip the whole shaping and attaching them to each other.