The concept of souls is metaphysical. They are not observable, so even if they exist (which not everybody agrees on, far from it), there's no telling that trans people are souls of one gender trapped into bodies of another gender. It would be literally impossible to know.
What if they do have a female brain
How could a man have a female brain? Female how? Not materially, since every single one of his cells has male DNA in it. Not in the way it works, since trans women still exhibits very specifically male patterns of behaviour after transitioning. So how would their brains be female?
even genetic effects that haven't been discovered
Don't let the TRAs hear you. An actual way to test for being trans is the last thing they want. Personally, I wouldn't care: either it would show I'm "really" trans, which... would change nothing to my life, or it would show I'm not trans according to that one test, which again wouldn't change anything to my life. Because at the end of the day, even if I have a genetic condition, I still can't change my sex.
Or could be due to hormone problems in the womb.
Or psychological issues? I think that one is by far the most likely, but funnily enough, nobody on the trans side wants to hear about it...