It goes waaaay way back before Sumer even. Babylon was at least centuries after the time of Adam and it's really worth reading The Book of Enoch (I'm part way through it), the things in there are amazing.

Put it this way, if the individual Adam existed, then he was at least predating the founding of Jericho, just to put a timeline on it. And the archaeology points to about 11000 years ago, which is also after the Dryas, which was caused by meteor strikes that slammed into western europe, the atlantic, north america and the eastern edge of the Pacific. So, since that puts a date for the Flood story to be coincident with the onset of the cold period of the Dryas, Adam must have been at least more than 13000 years ago.

This book, The Book of Enoch, was deliberately hidden and burned and forbidden and the ethiopian orthodox church retained it and from there it returned to us. And then it was found amongst the Dead Sea Scrolls as well, and more than a few parts of it are restated in books all through the bible, and many of Jesus' sayings come from it. One I already saw was "the meek shall inherit the earth" and another was the promise after the flood that it would not happen again. (shades of 5th element narrative haha, when they return, so shall we!)...

Anyway, it's more fun to dig it up yourself, but the book The Apocalypse of Yajnavalkya stitches together a very interesting story from Enoch, Thoth, Hermes, and of course lots of stuff relating to the Vedas, pointing out how all the myths have more than a few common points that suggests they are derived from original stories far older than is yet recognised.