Better term to put on a label of a bottle of milk to describe that it's 'made' in a particular geographic location
Dictionary.com says that milk is "liquid produced by mammals". Perhaps produced would be better. Cows "make" milk and they "produce" milk, and both sound normal and natural and idiomatic to me (American-speaker): either word should work. The problem for me with this advert is the meaning of "Permeate Free". What a strange name for milk!
I've seen labels like "Product of", "Produce of" being used on food labels and I think that it may be more apt in this case.