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Scholars surmise that a series of Sumerian legends and poems about the
mythological hero-king Gilgamesh, who might have been a real ruler in the late Early Dynastic II period (ca. 27th century BC)[1], were gathered into a longer Akkadian poem long afterward, with the most complete version existing today preserved on twelve clay tablets in the library collection of the
7th century BC Assyrian king Ashurbanipal.
Source:
Epic of Gilgamesh - Wikipedia, the free encyclopedia
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There is nothing definite about whether it is only a story, or when it occurred, but the story was recorded much later than 2700 BC according to scholars. This places the Gilgamesh story after the historic flood recorded in Genesis.