You can if you have a flood of epic proportions.
There were no single “flood of epic proportions”, as described and narrated in Genesis 6 to 8, no Noah living in the 3rd millennium BCE, no Genesis until the 6th century BCE when hostages of Jews lived in Babylon.
No portions of Genesis as a work of literature exist in the Bronze Age (c 3100 - c 1050 BCE), as there were no Hebrew alphabet existing until the Iron Age.
But there are long history of writing existing in Babylonia during the 2nd and 1st millennia BCE, eg Akkadian cuneiform writing system, and before that in Sumer in 3rd millennium BCE, where the earlier Sumerian cuneiform predated Old Babylonian period.
In Sumerian poem about Gilgamesh, specifically that narrated the “Death of Bilgames” are allusions to “Ziusudra” and to the “flood”, and some surviving fragmented tablets of the “Eridu Genesis”, which narrated Ziusudra’s story.
If you don’t know Ziusudra was the original name of the hero in Mesopotamian flood myth, while Bilgames is transliteration of Gilgamesh’s name in Sumerian (Gilgames or Gilgamesh is the Akkadian and Babylonian & Assyrian transliterated spelling).
During the Old and Middle Babylonian periods of the 2nd millennium BCE, Ziusudra was replaced with Atrahasis, eg Epic of Atrahasis, and with Utnapishtim, eg Epic of Gilgamesh.
The Epic of Gilgamesh was so popular in the mid-2nd millennium BCE, during the early part of the second dynasty in Babylon, that some tablets were found as far west in the cities of -
- Amarna (a city built in Egypt during 14th centuries BCE, during the 18th dynasty reign of Atenaten),
- Hattusa (a Hittite capital in what is now located in central Turkey),
- Ugarit (ancient city in northwest Syria, now known as Ras Shamra)
- Megiddo, an ancient Canaanite city, not Tell Megiddo in Israel.
The point being the stories of Ziusudra, Atrahasis & Utnapishtim, all predated the Genesis Noah. Genesis was most likely first composed during the Babylonian “Exile” in the 6th century BCE, when Jews encountered the myth of Utnapishtim.
The part about constructing vessel large enough to house the hero’s family and animals existed all versions of Mesopotamian myths, as do the smell of blood sacrifices reaching the gods; the part about releasing birds to find lands, survived in the Epic of Atrahasis and Epic of Gilgamesh.
Clearly, the Genesis version was copied from the Epic of Gilgamesh, and adapted to suit Hebrew readers.
The biggest differences between the Mesopotamian versions and the Hebrew version, is that in the Eridu Genesis and the later Epic of Atrahasis, it only described a river flood, the Epic of Gilgamesh described a sea flood. Whoever wrote Genesis exaggerated even further, with water covering “the high mountains”.
Beside all that, there are geologically and archaeologically, no physical evidence of single flood destroying all life, whether it be global flood or localized flood.
Plus, the post-Flood chapter on the Table of Nations, Genesis 10, the descendants of Noah, is a piece of pseudo-history, with no basis in reality, especially in regarding to Egypt (or Mazraim) and Nimrod in Babylonia (Shinar, eg Erech or Uruk) and Assyria (eg Nineveh & Calneh).
Uruk have been been dated as back as 5000 BCE, while Babylon have only existed as early as 2300 BCE. The earliest settlement in Nineveh been dated to around 6000 BCE, while Calneh, or Kalhu was a Babylonian city built during the reign of Shalmaneser I (began in 1265 BCE).
It isn’t possible that Nimrod to build any of these cities, unless Nimrod lived for several thousands of years; so Nimrod is fictional character, just like Noah.