You just don't miss a blowout of that size in the relatively small confines of the eastern Mediterranean. Ash deposits have been found as far away as Egypt and Turkey, and most Aegean islands have a charred layer of soil.
My parents were in the area (on my dad's WWII "victory tour") and visited Thera (modern Santorini). The island is just the surviving rim of an enormous volcanic crater (6-8 miles across), and they have a museum there with all sorts of neat stuff.
I don’t discount the Thera explanation for Atlantis but it is one of many.
The blow-out of Thera destroyed the Minoans but it didn’t bring about the end of the Bronze Age. What’s important to realize about Thera was that it was a crater with an island in the center before the Bronze Age eruption, not a mountain, with limited access from the sea creating the perfect sheltered harbor. The Minoans essentially build their Hong Kong right on top of an active volcano on the island in the middle.