The University I went to, Århus University, here in Århus, DK, uses A History of World Societies McKay, John P.—for the introductory course, basically making sure all students are up to speed—although it is used alongside more, or less, critical lectures with researchers from the relevant fields. So we have historical anthropologists and archaeologists doing the pre-history, classical historians for the antiquity, etc. etc. etc.

McKay is somewhat criticised, at least in Denmark, for being a very "American" book; not necessarily a bad thing, it is just out of the norm for how history textbooks are usually written in Denmark, and it is, at times, seemingly forcing through some weird formulations, to balance certain interests, etc. etc. but it is overall regarded as one of the best world history textbooks out there.

It starts with the earliest human societies and with hominid evolution, aka. with pre-historical humanity, so I don't think we get closer to the beginning. My coffee-smushed and somewhat tattered edition ends with the early 2010s as the finishing pages, so it gets quite close.