I can verify this approach works for me. The other thing I suggest is use "getting stuck" as a way to identify gaps - go look for books that fill those gaps.

Recently I cracked open Principle of Analysis by Rudin. I got stuck pretty much straight away and looked it up - I saw a few suggestions for a bridge between high school maths and the rigor required by that book. I'm now reading another book that took inspiration from the previously mentioned book but gives a bit shallower a slope towards the rigor required.