I think we are all putting the cart before the horse. Or, should I say, the cheese before the goat.
Cheese could not exist until humans began domesticating milk producing animals. These animals, goats and sheep, were domesticated for their meat and wool. The use of their milk would only have come about as an after thought.
And, what do we mean by "civilization"? If it's being used in the old sense of a society in a settled location and having a hierarchical structure - derived for the Latin civitas - then it was the cultivation of grain that was the prime factor. If we mean the development of art, religion and a complex social structure; then those things existed long before the agricultural revolution and perhaps before the rise of modern humans.