So gravy is typically defined as a meat stock thickened with a roux, which is made by combining flower and fat into a paste. The earliest mention I'm aware of is mentioned in a 4th-5th century Roman cook book attributed to "Apicius" a pen name that was associated with luxurious food. The entire collection of texts can be found in its original Latin and in English here Most I wouldn't recommend.

There are several recipes that call for what we would probably think of as gravy. The first one I could find is the first recipe in book VI, for boiled Ostrich. It calls for a number of interesting spices to be boiled with the bird, strained, and thickened with roux (amulo obligas in the original Latin) into a "gravy." As far as I know, written recipes from before the 4th and 5th centuries are few and far between, and this is the earliest written account that I'm aware of. If anyone is aware of earlier ones, I'd be interested to see them. I also can't speak to the origins of roux, unfortunately.