The wheel is old enough so that we don't have good written records, and early wheels are often not preserved archaeologically. However, we know that the wheel was invented at least twice: at least once in Eurasia, and at least once in America. We don't know exactly where or when wheels were invented; there are three common candidates for the Eurasian invention, and we don't know whether the wheel spread from one to the others, or whether there were multiple inventions.

For the invention of the wheel in Eurasia, see https://www.reddit.com/r/AskHistorians/comments/ayuy1c/is_there_any_way_of_knowing_which_civilisation/ which is asking the simpler version of the question - where was the wheel first invented? - rather than the more difficult "how often?"

For American wheels - which were invented independently of Eurasian wheels, we know even less of the details of their invention. American wheels appear to been restricted to toys: https://www.reddit.com/r/AskHistorians/comments/ay8al3/did_native_americans_before_columbus_discovery/