I think one theory is that it was central Asian horse-riding societies who started carrying milk on horseback, in saddlebags made out of animal bladders. The motion of the riding and  the rennet left in the bladders churned the milk and turned it into cheese.

I remember also reading on a science magazine’s site this possibility that the first cheese made by humans was more of yeast-based preparation, without animal milk, but i can’t find the article mentioning that anymore.