It never even crossed my mind that I was a girl before I found out what transgender was in my adolescence (though I always knew I was different) - is this normal?
I never knew transgender was a thing when I knew wanted to be a girl so I just started hormones out of curiousity and then figured transsexuality actually exists.
Why would yours not be normal?
Not very unusual at all. A very large minority of trans people don't "get" a clear idea of their gender identity until after puberty/into adolescence, and becoming aware of transition is a big kick in the ass to give it a little thought.
So, yeah. You're in good company.