I think you overplayed your ace a bit, also considering the flop was AQX, where AQ beats your AT as well and I did a 2.5BB pre-flop raise, which you then re-raised to 5BB. But tbf it's always super hard to spot a set - one of the hardest things in Poker (for me ?). On lets say a AJ3 flop, that 3 looks like a blank, but can actually mean a super strong hand for your opponent. In the end it comes down to all this again:


I think even the best players are struggling to spot sets, but they are doing much better in anticipating the possible danger, be it via analyzing pre-flop raises, post-flop bet sizes, experience or pure gut feeling.
Problem is, when you concentrate too much on possible sets, you will just see them everywhere on any given flop They are curse and blessing at the same time - and if I was asked to do new rules, I would eliminate them