Without this interaction with this external categorization: would you have been able to find anything was “different”?
Yes.
The words I use to describe it would be different. If I grew up on an island of men, I’d have been completely lost trying to understand it, and may never have found the words, but I would still have felt it, because I was already feeling it before I had the words.
Trans people are real. Our experience of gender is real. Those experiences don’t align with yours, but that doesn’t stop them being real. Trans people exist in one form or another, across every civilisation, and have done so through the length of recorded history.
You won’t find a “gotcha”. You won’t make other folks experience match yours, just because you don’t understand theirs.
Stop trying to tell me my own experience. You don’t experience gender. Stop trying to speak for people who do.