The 1628 BC date for Thera was arrived at less than ten years ago, and is based on a reckless disregard for Carbon-12 enrichment of both soils and artifacts made from plants and trees grown in those soils. The estimated date for the supposed supereruption was 1500 BC, and that was the estimate by no later than 1950 AD.
The supereruption has literally zero literary remains; from ancient sources written right on top of what should have been the action, we have no preserved legends whatsoever. In the 19th century, someone dreamed up the idea that there was an eruption there and that hypothetical event wound up associated with Plato’s Atlantis.
The pipsqueak island of Santorini has a submerged caldera with one side gone, but the age of the caldera is very much prehistoric (20K or older). The only eruption recorded from classical times works out to circa 200 BC. That’s all there is.
I attended a seminar in 1987 where we were told that ash from Thera had been found in the Greenland ice cap and that the ice core yielded a date of 1628 B.C. (or perhaps it was “about 1625” and I got the 1628 date later). It wasn’t from carbon dating and it definitely was much longer than 10 years ago. I know they used to date the eruption rather later than that.