They arrived at about the same time but the result helped develop civilization. Rather than people being nomadic, the cultivation of grain helped stabilize civilizations with the development of grain-based agriculture technology. 

The two main grains used by ancient peoples in brewing and baking were barley and a kind of wheat known as "emmer". The original first beers made from raw grain were very low in alcohol, using the small amount of natural sugars available in the grain. Sometimes the water used wasn't always potable, so low-alcohol beers became the drink of choice; the low alcohol content killed any pathogens that might harm a person. It was safer to drink the beer than the water! 

A big step ahead came (around 3,000 B.C.) when the brewers in Mesopotamia learned to turn barley into malt--probably accidental at first. Raw grain was wetted then left to dry in the sun. The grain would swell in anticipating of sprouting, then it was dried while it still retained its rich sugar and starches. Now the fermented beverages made were much higher in alcohol. The process of making malt became more sophisticated, and the Mesopotamians were able to produce dark and light beers; a darker malt was made by slightly scorching the malt over a fire. 

Early brewers knew nothing of yeast; they did know that when they made beer, the deposits from previous brews left in their clay pots would turn the liquid into alcohol. Wild yeasts also contributed. Hops weren't used at this time--the plant was not known. The brewers made "beer bread", and poured heated water over the bread, which was filtered and left to ferment spontaneously. 

By Bitter Root Brewing.