Based on my reading, yes.
The ancient historical record is far from what we'd consider sound documentation, being merely a chronicle and king list. But the first political entities also seem to have been the first cities, Ur, Lagash, Larsa, Isin, Eridu, Kish, Nippur, and others. (It might be more proper to say that they were ruled by priest kings instead of just kings, but by all means see the link below for more detail.)
Subsequent history records leaders who emerged and sought to unite them into a larger empire.
Edit: My esteemed colleague Lucio Margherita has suggested that some rough dates might be helpful, and has thoughtfully provided them:
"First settlement in Mesopotamia 5000 BC.
Hunting gathering to 3500 BC
City states to 2500
Sumerian/Babylonian empire and list of kings after 2500."
...Thank you, Lucio, although please note that our knowledge from these times is very incomplete. Archaeological discoveries at sites such as gobekli tepe suggest that there may have been much activity that we would classify as civilization occurring much earlier that was previously thought, outside of the historical record, or such of it that we have.