Some believe that the Sumerians were not native to that area and were from places in the east. Refugees from Sundaland?
No doubt they were following the herds North from Sundaland as the Ice Age ended and Sundland was gradually covered with water.
Folks speaking a cognate language went all the way to Norway following the herds ~ most likely reindeer.
Later on Semitic and Indo-European speakers moved in on their territory. They were reduced to being "scribes" while the Semites and Indo-Europeans went about creating Babylon and Persia.
I suspect the Sumerians made a good living out of the "scribe" business for the next few thousand years.