In a TV prog called "What the Ancients did for us" - they showed the Mespotamian method for brewing beer (as Adam Hart-Davis called it) and he asked the head brewer of Shepherd Neame about hops. His reply was that hops were not introduced until the 17th century.
But then he was on the prog for the advertising potential of a brewery started in 1682 (nb). Perhaps he was referring to the widespread use of hops. I think it was Shepherd Neame that made the Egyptian "boutique" beers recently.
The Mesopotamian brew would be an ale anyway - barley, wheat, bread (a barley/fig mix) and honey.