The spoken languages and written languages are learned processes, are matters of linguistics and philology, not the studies of theory of Evolution.
Existing parallels to Sumerian civilisation throughout the 3rd millennium BCE, was the Egyptian language, west of Sumer, and in the east, were the Indus Valley Civilisation (IVC) in South Asia. But there were hundreds of different cultures with their own distinct spoken languages that we don’t know about, because they were illiterate societies.
You are only focusing on “civilisations”, but outside of Sumer, of Egypt and of IVC, there were hundreds, possibly even thousands of different cultures, each ones with their own spoken languages. There were already Semitic-speaking people dwelling among the Sumerians, like the Akkadians and the Amorites during the 3rd millennium BCE. So when Sargon of Akkad (founder of the Akkadian dynasty and empire) conquered Sumerian cities during the 24th century, they have adopted some of Sumerian customs, including Sumerian cuneiform writing.
The Sumerians were also aware of the language spoken by the Elamites, who dwelled in western Iran. like the Akkadians, the Elamites didn't have their own writing system, so they too eventually adopted cuneiform.
The Helladic people of the Aegean civilisation (which included Crete and mainland Greece), have their own languages during much of the 3rd millennium BCE, but they didn’t have their own writing systems, until the 2nd millennium BCE, eg Linear A, Linear B.
At no time, were there ever global flood or the Tower of Babel, where the entire world spoke only one language…the Tower of Babel is a myth.
You have one-sided view of history…but Genesis isn’t a document of history.