Well the problem is that once you get past a certain time period, you start to run out of sources. Writing was incredibly rare before the 1st millenium BCE and only existed in certain civilizations. It's not a coincidence that we know more about Greece, Egypt, Persia, Babylon, etc. rather than other civilizations. They were the only ones keeping records! Other civilizations only have oral histories, which are certainly interesting but of highly questionable accuracy.
Also the reason why written sources are more numerous and accurate after around, say, the 6th century BC is because that's when people started writing everything down! Although writing existed before then, there was a massive increase in trade during that time period and that's when writing became commonplace. Scholars believe that was the time period in which the Greek legends as well as the first books of the Old Testament were all written. So there is a period ranging around the 6th century BC to the present where we have continuous (and thus accurate) written history being recorded, a written history of the oral traditions of those cultures (that goes back some time but is of questionable accuracy), and then a time of prehistory where we have no information other than what we can put together from archaeological data.
If you look at that wikipedia page you linked, almost all of those dates are based on archaeological data. The way that works is an archaeologist finds a site that looks promising and starts a dig. They find any artifacts in that area, analyze it, date it, compare it to other sites in the region, and extrapolate information based on that. Other scientific fields are also used to help out: chemistry, genetics, linguistics, anthropology, climate science, all of them are used in constructing history. But that's not very precise and extremely dependent on finding good archaeological data, so that's why you have the lack of precision.
Go back 2,000 years and there is quite a bit of archaeological data. Go back 5,000 years and it is is very hard to come by. Go back 10,000 years and it's practically nonexistent. That's why we know so little of prehistoric civilizations. There's literally no other information other than "There were people here, and they left these types of tools" and maybe some bones or cave paintings.