If there's one thing we know it's not, it's those kinds of floods, because those you talk about come from Ice Age and giant glaciers sliding or breaking down giant lakes. There was none of those in the Middle East when humans existed, not in Mesopotamia which is a giant flat plain, and that's where those stories came. We know the biblical account is a copy of the Sumerian account, and we know what event the Sumerian account comes from. It's not an Ice Age story, and it doesn't come from an earlier, older memory from WAY further North. The closest event to that is indeed the Black Sea expansion that happened at the end of that period, and we know that one took a few thousand years.

The period of the Babylonian captivity, when they were brought to Babylon as prisoners and stayed several decades through the 6th c. BCE before being freed by Cyrus II, is likely a point where they brought a lot of Babylonian culture back to Jerusalem. Plus, the god of the Bible comes from two origins, Yahweh and El, the latter being a storm god that had a lot of cultural osmosis in the entire second millennium BCE, being associated with Enlil and Baal, through whom the Sumerian and Akkadian stories did get around. So there's definitely a part where some of those stories made their way into Canaanite culture by themselves, then the Hebrews and Jews, naturally over several centuries to become their own ancestral culture, and a part where the Jews brought back and adopted Babylonian stories when they returned from the exile. We can tell because of the narrative / writing style and the variations that we can find, we can date when some of those stories appeared.

In the case of the Flood story, the text has too many similarities, identical lines, to not be straight up copy-pasted from Babylonian texts after the exile - but even then, there's a couple variations of the Biblical story that does suggest they already had a memory of that story in their own culture (40 days or 7 days, that sort of details). It's fairly likely that they simply considered that those stories were about the same god as their El, in the same way the Greeks would go "oh, you have a god of thunder too? I bet his name is Zeus. I like your story about Zeus." And really, they're not wrong, since they do have the same origin, they are in fact the same god, branching into many cultures across Mesopotamia over a couple millennia.

So no, they definitely didn't know anything about the actual event that inspired the deluge story (you can tell by how it's all an abstract threat to them, because the Jordan river doesn't flood anything like the Euphrates, compared to the real threat and pain of exile), but they knew about the story of the deluge.