I wonder how rapidly the change occurred - were the people aware of it happening? Did they have people saying “don’t listen to Yarg! These recent floods are just normal weather…”
At that time time they were still hunter gatherers. So they might have been aware of their surroundings, but I presume not as much if they would have been a sedentary community.
The first communities started to settle more or less after the ice age ended, the sea level had risen and the planet had a more pleasant climate around 10000 years ago (source: I'm not a professional on this topic, just summarising what chatgpt tells me)
It was a relatively sedate 2m per century a lot of the time, but there was one catastrophic Tsunami event called the Storegga Slide around 6200 BC that would have been pretty dramatic.
similar doomsday predictions were made and went unfulfilled im sure, much like modern times
My uneducated guess is: probably not before writing was invented. Populations where nomadic, changes were likely slow and life expectancy was much shorter. With no record keeping it is unlikely they had means to notice the changes.