Generally speaking, people usually say the first Civilization was Ancient Sumer. But when you actually look into its history, there are in fact different city-states (Ur, Uruk, Lagash) that all appear to be independent of each other.
So it begs the question, was Sumer actually a singular and unified Civilization before the rise of Akkad and the Third Dynasty of Ur, or is it just a general term for Mesopotamian Civilizations to avoid any complicated Ancient politics?
After Sargon conquered it, yes. Prior to that it was just a collection of independent cities trying to survive in the marshland. Occasionally one city would conquer another, but that typically would not last very long. The Sumerian army essentially consisted of (at best) 300 men wearing leather capes armed with cattle prods.