My crazy theory is that a maritime civilization grew and flourished in regions which are now under one or two hundred feet of seawater, and that the end of that civilization came surprisingly quickly as the glaciers melted. This then is why what I would call “fully developed” civilizations mark the beginning of civilizations as identified from the archeological record. They were the descendant cultures of those which had been washed away.
/tinfoil
The continental shelf must have loads of evidence, more than has already been discovered. Probably not a single worldwide civilization, but people have been using watercraft of some sort or other for 100s of 1000s of years. Even if there wasn't some thallosocracy, there were ships on the waters.
The Anatolian site Catal Huyuk thrived because of the terrain and its control of the overland obsidian trade. Related, smaller towns in the region were similar in building style, but it has been suggested that the lack of development in the lower strata of all these sites -- as if they just popped into being -- implies a period of development elsewhere.
Since that's never been found, the proximity of the Mediterranean probably means their forebears lived on what's now the shelf.