I am corrected: Yes,the Black Sea level was much lower, and rose. But how quickly? E.g., if the Bosporus was blocked, and later broke, the water could rise very quickly, over weeks, not years. It could fall, instead, if the sea had filled in, and then suddenly drained by a similar process.
But the subject is complicated by the unknown inflow from rivers, and from meltwater of retreating glacier.
Hydrology is complicated.
Evidence of catastrophic flooding is debated and inconclusive.
That the black sea’s level used to be much lower is not, all water levels were much lower at the glacial maximum, and gradually rose as the ice age ended, nearing stable historical sea levels around 7.5kya (5500 bce).