A battle took place in Hamoukar some time around 4,000 BCE or 3500 BCE at the latest. Small stone projectiles worked into spheres have been uncovered in the ruins of this ancient city. Moreover, walls were found that seem to have corresponding damage, so it looks like the projectiles were left behind by Hamoukar's enemies. The attackers are presumed to have been the Uruks from Mesopotamia. Still, there is no writing to prove it.
Then, there comes Sumeria and writing. Sumerians left behind carvings that clearly depict men in battle dress and formation. So, by the time we could write, we not only had battles, but an organized military! Now, the two may have emerged around the same time, but evidence of fighting goes back so far that it is likely we had organized military groups before we even invented writing.
Sumeria certainly had her wars and from there, the history of man is the history of war. Nary has a civilization existed that does not conquer or be conquered. Be the cause resources, madness or even love, war is one of the few constants for humankind and will likely always remain so.