A good theory but the time span is a bit long even given a 5,000 year transition. The last ice age ended 25,000 years ago.
https://www.cdm.org/mammothdiscovery/wheniceages.html
There were at least 17 cycles between glacial and interglacial periods. The glacial periods lasted longer than the interglacial periods. The last glacial period began about 100,000 years ago and lasted until 25,000 years ago. Today we are in a warm interglacial period.
Another interesting theory, but even longer ago, is when the dam burst at the Rocks of Gibraltar and let the Atlantic into the Mediterranean basin. Kinda like flooding Death Valley with the Pacific if it was closer.
https://www.sciencedirect.com/science/article/pii/S0012825219302521
About six million years ago, the Mediterranean Sea underwent a period of isolation from the ocean and widespread salt deposition known as the Messinian Salinity Crisis (MSC), allegedly leading to a kilometer-scale level drawdown by evaporation. One of the competing scenarios proposed for the termination of this environmental crisis 5.3 million years ago consists of a megaflooding event refilling the Mediterranean Sea through the Strait of Gibraltar: the Zanclean flood.
Although I don't know how they'd know at the time, it's possible ancient humans found signs of flood...or just fossilized seashells and "theorized" a great flood much like some found dinosaur bones and "theorized" about dragons.