i'm curious as to what verbal cues your daughter gave you at 3 1/2, that called serious attention to her identity.
The most impactful was when she talked about her male persona being a stranger to her and expressed some pretty grim dread and depression. Since we acknowledged her, she has been much better. She's a normal kid now.
There is a lot more to it. From very early on she expressed a strong dislike - a revulsion, really - for the start gender definitions you find in regular things. Spend a little time looking for clothes for a 3-4 year old. Or go to a Hallmark store and look at birthday cards. It was startling to me to realize that your basic stuff like Hallmark cards and Carter's clothes is annoyingly divided into truck vs princesses. Anybody who cannot grasp the amount of gender conformity going on from birth isn't paying attention or is clearly an idiot.
Our little one is smart. She picked up on this immediately and wasn't having it.
And frankly, she isn't into the princess thing. "He" used to really dig trucks but the fascination quickly waned. We have a shit ton of really nice Bruder's trucks but she just lost interest. She still plays with a lot of traditional boy stuff. We play with soldiers and forts a lot,, cowboys and indians versus zombies.
I do believe that there is a genetic component. Her mom and I are both a bit gender bending in many ways. I know some others won't believe it, but we did nothing to promote her views but we certainly didn't promote strict gender roles either.
Perhaps you could blame it (go ahead, I don't care) on being exposed to glam music too early.
Yesterday I went out for an errand. I told my wife "if while I am out, I am killed by a plummeting 747, promise me two things: one, you will introduce her to the Velvet Underground at the appropriate time and that you will get her into a good art school (she is talented)". The fact that this would make me happy is perhaps telling. Most "men" in this region would consider it a nightmare. But all they really talk about here is sports and their zero-turn radius mowers.