There is reasonable evidence of some male-female differences in brainsbut a spectrum, rather than an either/or difference. I have no doubt that you will see some gender^atypical traits in gender-nonconforming people. But that doesn't mean they "are trans"it means they are gender-nonconforming.
The question is, should this person be encouraged to live as a gender-conforming member of the opposite sex or should they be steered towards living as a gender-nonconforming member of their own natal sex?
That is a tricky question. It has nothing to do with their being "trans" brains.
I think it is a mistake to think of transgenderism as being like homosexuality/heterosexuality.
Being attracted to your own natal sex appears to be fairly set-in-stonethere is no evidence that conversion therapy works, and the % of people who are attracted towards their own natal sex appears to be fairly consistent worldwidecross-culturally, about 3.5% for men, around 2% for women.
Being transgender, by contrast, is highly culturally malleable. The rate of transgenderism varies enormously from society to society and from time to time, and it appears to be linked closely to social beliefs about gender roles; generally speaking, the more rigid/binary a society is about gender roles, the higher the rate of transgenderism tends to be (hence, many TG people in places like Brazil where there is a macho culture for men. It's hard to live as a gender-nonconforming femme-y man in such places).
Take, for example, the case of a biologically male person who is attracted to men and is gender-nonconforming (likes cupcakes, soft furnishings and other things that are more associated with women; gestures and voice are often clocked as "feminine"). That person would live as a gay man in many societies. In other societies, that exact same person would probably end up living in the role of a woman, with or without surgery.
The trans issue, therefore, requires us all to think carefully about what kind of society we want to be. Do we want to be tolerant of gender-nonconforming and gay-ness, and be the kind of society where most GNC just live as GNC members of their own sex? Or do we want to be a society of more rigid gender roles, where a high percentage of same-sex attracted, GNC people instead choose to live in the role of the other sex?
I have no doubt that there will always be a certain number of people who are very gender nonconforming and find it hard to live that way, and therefore feel it is a better choice to live in the role of the other sex, and I am glad the surgery, hormones and other things exist to help this to happen.
I also believe thatfor the sake of GNC people themselves, and for the sake of society at largeit is better in the long run if we work on the assumption that most GNC people can live healthily and happily as their own natal sex, and that you don't have to rigidly conform to every rule about bras and shaving and hair length if you don't want to.
First port of call for young girls like this should be to talk to her about how she can be a woman any damn way she wants to be--it's fine not to pluck and shave and wear skirts if she does not want to.