Even if that would be true about the text that we have found, it is possible that we just have not found the oldest scriptures. Hebrews can have had the message transferred orally much longer.
The Sumerian Flood story is actually already based on centuries older oral tradition of Ziusudra, before it was written down 24th-22nd centuries BCE.
Floods occurred annually along wither Euphrates and Tigris, which were usually not to severe and that helped with depositing fertile loam (due to erosion of soil, north of mwith irrigating the land, but the legend of Ziusudra was actually based on a real 29th century BCE flood, that was more destructive, and evidences were found in the Sumerian city Shuruppak.
2900 BCE marked the end of Jemdet Nasr period (c 3050 - c 2900 BCE) and the beginning of the Early Dynastic I period (or ED I, c 2900 - c 2750 BCE).
The Early Dynastic period ended with ED IV about 2350 BCE, with the start of Sargon of Akkad, known as Sargon the Great, reign c 2334 - c 2274 BCE. Sargon was founder of Akkadian dynasty and responsible for the Akkadian empire, the first true empire.
The Akkadian period (c 2350 - 2147 BCE) and the 3rd dynasty of Ur (known as the Sumerian Renaissance, c 2047 - 1940 BCE) saw the flourishing of both Akkadian and Sumerian literature. It is around these times that we have literary evidences that oral traditions were transmitted into written literature.
Lots of Sumerian poems were written, including the creation and flood myth Eridu Genesis and the earliest Sumerian poems of Gilgamesh (particularly the tablet known as the Death of Gilgames), which Ziusudra appeared in both.
The thing is the Genesis 10 claimed a number of cities were found in Shinar (Babylonia) and Assyria, by Nimrod, a great grandson of Noah. No such person existed in Mesopotamia.
For instance, Sargon was born in Akkad, a city that Nimrod supposedly built. Sargon was a real historical figure, Nimrod is purely mythological and fictional character.
What you don’t seemed to understand 1213, is that many of Sumerian cities predated Sargon, and some even predated the Sumerian civilization (3050 BCE), like Ur and Uruk, both of which existed 2000 years earlier.
Genesis 10 claimed that Uruk (which some translations of Bible called Erech) didn’t exist until after the flood, but archaeology showed that the earliest settlement of Uruk (referred to as Uruk XVIII) were inhabited as early as c 5000 BCE.
Uruk, like many cities in the Near East, newer settlements on top of earlier settlements.
Throughout the 4th millennium BCE (4000 to 3000 BCE, which are Uruk XVI to III), Uruk was the most important city in Mesopotamia. Temples were built to the goddess Inanna in the Enanna district of Uruk, between 3600 to 3300 BCE. In the Anu district, a stone temple, known as the White Temple, was built on top of the Anu ziggurat.
Furthermore, if there were Noah’s flood around 2350 or 2300 BCE, then there should be evidences of flood stratum and debris in Uruk, Ur, Kish and other cities, dated to the same time. There are not.
Clearly what Genesis say about post-Flood and Sumerian cities are wrong, historically and archaeologically.