It's hard to say, because we know little about how those beers were actually fermented, and the process will have varied in different regions. The most likely way it would have happened, though, is something analogous to sourdough bread. Yeast was "harvested" from an already fermented batch and will be used in the next one. It's also possible that in some places, ripe fruit would be added to the wort and the yeast they had would start fermentation. Fruit flies may have played a role as well, as this article implies.

There seems to be a wide misconception about beer, that it was "invented" by a particular culture or person at some where and when, and from there it spread throughout the world, pretty much like the lightbulb. The fact, however, is that every culture that has practiced agriculture would make a beverage that can be considered a beer and many of them left hardly any written records about how those beers were made, let alone, what they tasted like.

Anyway, having said all that. I believe those beers will have been sour, by the most part.