Baby geologist here. You don't need a flood. You don't need anything exceptional. As ice ages develop, sea level goes up.
Well, let me actually clarify a bit--the coastlines go up. There's less water in the oceans--it's all turning to ice through the precipitation cycle--but the shores still go back up the coast anyways.
Why? Well, because rock's a fluid on geologic timescales. Imagine you're in a boat, and then somebody puts a bunch of stuff in it: the boat's going to settle. In this case, the continents are a boat floating in a sea of rock, and all the ice developing is the stuff. We call this state isostasy, and when you add ice to the continents, you disrupt it.
That's right, baby, it's isostatic depression. When you cover the planet in ice, the continents sink into the earth a bit & the coastlines go up, by up to 200 m during the last ice age.
The opposite is also why sea levels are still falling on Canada shorelines
today--North America is still rebounding after all the ice came off a short 10s of 1000s of years ago.
EDIT: Surprised to see downvotes without comments. Added some sources for you skeptics.