Ngimun, Yidyam, and Barany are crater lakes in Australia. There's a story of how they came to be:
It is said that two newly-initiated men broke a taboo and angered the rainbow serpent Yamany, major spirit of the area ... As a result 'the camping-place began to change, the earth under the camp roaring like thunder. The wind started to blow down, as if a cyclone were coming. The camping-place began to twist and crack. While this was happening there was in the sky a red cloud, of a hue never seen before. The people tried to run from side to side but were swallowed by a crack which opened in the ground'....
.. After telling the myth, in 1964, the storyteller remarked that when this happened the country round the lakes was 'not jungle - just open scrub'. In 1968, a dated pollen diagram from the organic sediments of Lake Euramoo [Ngimun] by Peter Kershaw (1970) showed, rather surprisingly, that the rain forest in that area is only about 7,600 years old.
Some other stories refer to places that haven't been above water in 9000 years. "The stories tell of a river that entered the sea at what is now Fitzroy Island. The great gulf between today’s shoreline and the reef suggests that the stories tell of a time when seas were more than 200 feet lower than they are today, placing the story’s roots at as many as 12,600 years ago."
"In one of their stories, Ngurunderi chased his wives until they sought refuge by fleeing to Kangaroo Island—which they could do mostly by foot. Ngurunderi angrily rose the seas, turning the women into rocks that now jut out of the water between the island and the mainland. ... a time when seas were about 100 feet lower than they are today, which would date the story at 9,800 to 10,650 years ago."
The Aborigines apparently have some careful crosschecks to make sure stories don't change: some stories are sacred and must not be adapted by the storyteller. Some of these stories match the ancient landscape nicely--the settings match.
What doesn't quite match is the action. OK, the volcano erupting is a pretty good description of what you might see. But the ocean levels weren't supposed to rise that fast. Stories of a woman crawling along dragging the water after her, or of Ngurunderi angrily raising the sea, are dramatic. That's either something that happens within a human lifetime, or something made dramatic by foreshortening. I'm not sure what would jump a shoreline 20 meters in a human lifetime: Lake Missoula draining won't do it (I estimated about 1mm rise from that). That amount of water draining off the glaciers that fast ought to have done dramatic erosion which we don't see. Great glaciers deciding to up stakes and slip-n-slide to the ocean would have turned the southern US into a Canadian Shield. Could 20 meters happen in a hundred years? My geologic skills aren't good enough for me to say.
That leaves foreshortening. What does that mean in practice? Cast back a few millennia. Stories from 1000, 200, 100 years ago illustrated landscape changes that needed to be explained. Assuming the rock formations were already regarded as women, somebody then synthesized the revised story from the old ones. Although this isn't the sort of thing they do, remember? Otherwise how would the details have stayed intact? Which leaves the option that the story was created at that time. It had to start sometime, of course. But the faster the sea level rise was, the less time was required to keep the stories intact, and the if they didn't need to keep them intact long, the more flexibility ancient the story-tellers/memorisers could have had compared to the modern ones.
UPDATE: I forgot about Lake Agassiz, which raised sea levels several meters when it drained in O(8200) years ago, and presumably also the earlier drainages. Not quite 20 meters, but if as supposed it happened over a few decades, people would certainly notice.