One has only to look at how many christians don't share all their worldy goods in common to understand that there are many, many muslims who are fond of alcohol.
In Barber's Women's Work: The First 20,000 Years she mentions that proto-Indo-European language reconstructors are pretty sure that besides the usual set of animals and weather conditions, there was a PIE word root for "getting high". I'm guessing literacy (~3'400 BCE), not existence of drinking games (~4'000 BCE?), will be the major driver behind "earliest documented".