see, i don't see anything particularly infeasible about early civilizations being flooded, but it's not necessary to go as far back as the ice age to get a flood scenario. the neolithic revolution, itself, would have lead to circumstances similar to what we're seeing today as "global warming". you just need to take your timeline forward a few thousand years to make it consistent with everything else. then, you'd have early neolithic sites being drowned as a consequence of the neolithic revolution itself.

the thing is that it's going to be difficult to separate the anthropogenic aspect from the natural one because they would have happened in quick sequence. but note that oceans continued to rise until ~6000 bce - well after the technical end of the last ice age. if you take it up to that point, it's no longer an outlandish date for early advanced settlements.