Wine is much easier than beer, because ripe fruit will ferment on it's own. Even wild animals get drunk sometimes; it's sometimes said that wine was discovered but beer was invented.

So alcohol without any grain is easy, but I don't know the answer for beer. On the other hand, why would you domesticate grain unless you already knew you could turn it into beer or bread?

Grain can be turned into porridge (so basically just soaked) and eaten, bread and beer is optional. In fact, IIRC classical-era armies would eat their grain as porridge instead of spending hours in camp baking it into bread. For obvious reasons.