Mesopotamian region experienced major flooding at the end of the ice age. A citation from a text of Jennifer Pournelle:
“vast rivers fed by melting ice and heavy rains carved their way through the earlier sediments that infilled the alluvial basin between the Zagros mountains of Iran and the Arabian plateau…”
That period seem to have happened ‘too early’ for the story. Yet, it seems that the period with higher precipitation continued until the fourth millennium BC, when the first urban cities formed in the Sumerian plains.
The silty plain was shaped and reshaped by an “interplay of tectonic uplift and subduction with rising and falling sea levels, rivers and floods, and windborne sand”. Temporary damming of a river is a realistic scenario but might not have been enough to flood the whole plain.
Writing developed by the end of the fourth millennium BC (the Uruk period). There are few texts from the early period of writing and these are mainly short notes related to administration, labor and commerce. That makes the early period prehistory rather than history, because we do not have sufficient texts from that era.
The Sumerian king list divides the history into the ‘pre-flood’ and ‘post-flood’ dynasties. Although the list of ‘pre-flood’ rulers may be at least partly mythological, the ‘post-flood’ list is associated with a period without massive floods - smaller floods were common but nothing that should have devastated everything. The dividing line was at the end of the rule of the city Shuruppag, with king Ubara-Tutu and his son, Ziusudra (= Utnapishtim). The flood was followed by the rule of the city of Kish. In the Epic of Gilgamesh, Utnapishtim and his wife are described as the only humans that survived the flood.
If there is any historical reality behind the mythical Mesopotamian stories about the flood, finding the year when the power switched from Shuruppak to Kish and when Utnapishtim lived would give a year for the famous flood in the Mesopotamian stories (which may have been a different flood than the flood of Genesis). It has been claimed that Utnapishtim lived around 2900 BC, corresponding to the flood deposits at Shuruppak between the Jemdet Nasr (Uruk III) and the Early Kingdom periods.
The interpretations about the early history of Mesopotamia have been guided more by opinions and expectations than actual evidence. The evidence we have from the Uruk period is mainly partial remains of structures and ceramics. Some amount of archaic texts have been found but they seem to be from the end of the Uruk period, with no certainty about the dating. The interpretations about the scanty findings have not been fully reliable - the facts have often been forced into an existing opinion or framework about the history, rather than vice versa.
The cuneiform texts telling the Sumerian stories are from much later periods, from Akkadian to Babylonian eras - hundreds or thousands of years after the early Sumerian era (Uruk period). These later texts are either mythology or mythologized history, so not very reliable.
I expect that the near future will give more information. There are vast numbers of cuneiform tablets in museums and other collections, a minority of these have been translated and published. Archeological work has been limited because of the geopolitical situation in the southeastern Irak. If there comes an extended period of peace and the archeologists get permissions and funding for the excavations, we will get more knowledge of the relevant period.