Think of the civilizations or the ruins thereof that were covered with water when the ocean entered the Black Sea. The Black sea gained something like 300' in depth in a very short time.
Yup. Ryan & Pittman, in their book, Noah's Flood, estimate that after the break-through, the water of the whole sea rose at the rate of one foot per day.
Most inhabitants would have been able to walk away with most of their animals and what-ever they could carry with them.
They think these hundreds of thousands, maybe millions of refugees streamed up the river valleys and spread farming and the Indo-European language all across Europe.
I've tried to connect these refugees to the 4,000 year old Caucasian mummies found in the Chinese desert. Some have even speculated that they are the same people who became the Ainu in ancient Japan (10K remain today) that replaced the previous Caucasian featured people there known as the Jomon.
BTW, the present day Ainu are the hairiest humans on earth.