But there were actually three (or even more) sunken landmasses that were really significantly big; nearly continent-sized. Check out this podcast, for instance.
Sundaland, Doggerland, and Berengia. Sundaland was an India-sized peninsula going down from Southeast Asia to the Wallace Line; today, only relatively small sections of which survive as Indonesia and other small island nations of the East Indies; and probably a major refugia that Eurasian populations grew from in general.
Doggerland was a massive continental shelf that filled much of the North Sea and even the area to the west of the British Isles, which largely was significantly (and probably very quickly) flooded; and was probably the highest population density in Europe during the Mesolithic.
Berengia was not as cold as you would think; relatively dry steppelands and very rich. Oh, sure, it was cold, but it wasn't ridiculously cold to the point that it was impossible for people to thrive there.
I'm always curious about what (if anything) could be done with this kind of stuff in alternative history stuff, but I'm also never quite sure what it would be.
As an aside; there was a transition in the Mesolithic to Neolithic where people lived shorter lives, were themselves shorter and more robust, and were unhealthier. Believe it or not, the hunter-gatherer lifestyle seems to have been healthier, although naturally it has a lower carrying capacity for population.
In Europe, at least, the Neolithic Revolution also is associated with a new population type, and probably associated with climate change. In other words; the hunter-gatherer lifestyle was better for us, but as we reached a certain carrying capacity and the climate changed, giving that up was the trade-off we made for continuing success. Plus; because the carrying capacity of communities is higher with agriculture, agriculturalists were probably able to dominate the small bands of hunter-gatherers militarily.
Until pastoral nomadism came along. Anyway, the Younger Dryas is the climate event that is often linked to the development of agriculturalism, but the reality is that climate pulses explain all kinds of changes in history. There are climate change pulses all throughout the archaeological record. Tons and tons of them. The Younger Dryas may have been a more dramatic than most of those changes, but not necessarily—the Little Ice Age and the preceding Medieval Warm Period were dramatic as well.