The Mediterranean last refilled five million years ago. Anyone who finds archaic human remains that old will next find the egress sign for their careers.
An ice age drop of 400 feet (or 800+ nearer the poles) didn’t cause dry land bridges to appear (apart from the Bering Strait, maybe some Arctic islands, but not Antarctica AFAIK) to link major landmasses or most offshore islands.
If the ocean was 400 feet lower as little as 20 to 40,000 years ago, than the Mediterranean would have also been about that much lower, as the Straits of Gibralter are at least that deep. I would like to see a map of the Med. with that much reduction in water level. I am sure it would show that there were islands not that far from main land at that time.