There’s no scientific research on this. Until very recently, the whole idea of “gender” was exclusively considered to be social - eg. gender was understood by social scientists to be the social networks of ideas that ascribe “femininity” or “masculinity” to particular ideas, presentations or behaviours — so, pink, long hair, makeup, being demure, staying at home with children, are all socially constructed ideas of gender. Also used to be known as “sex roles”/“sex stereotypes”. These also change over time in obvious ways - what is considered masculine or feminine is different in different eras. Second wave feminism (and lots of third wave feminism) was keen to dismantle or change sex roles and gender stereotypes.
In very recent years, this has become ideologically internalised so that “gender identity” no longer means something like “the gender roles I perform socially”, and something more like “an undefinable essence of gender residing in my soul/mind/inner identity” etc. This is more akin to a religious conception of the self/soul than anything you could measure scientifically.
Think about all those experiments from the sixties to the present that showed that gender stereotypes were inculcated and performed to babies/children from birth - eg. that caregivers responded differently to babies dressed as boys compared to babies dressed as girls and so on. All the actual science from the last century suggested that cultural and social gender roles start to be enforced very early on — these tended to suggest that gender roles (as opposed to sex) are largely socially produced, not innate. All that science directly contradicts the new religion of “gender identity”.
Think about a comparison with “national identity” (or other forms of social identity). We’d laugh at the idea that we all have an innate national identity ingrained in our soul (something that was, however, fervently believed in the nineteenth century). We understand that national identity is a set of cultural and social beliefs and narratives. (In fact, we used to understand that “identity” itself is a process of affiliation to particular cultural stories, values and beliefs.) We used to think about gender in similar ways, too, until very very recently, when gender ideologists promulgated the notion of an innate gender identity as some kind of inner transcendent essence (which could not be discovered by science even if science was bothered to go looking, since it’s essentially a kind of mystical entity).
There’s a wider process afoot in society where certain kinds of “identities” or aspects of identity are reified as innate essences when this suits some agendas (though some aspects of identities we still understand as social — it’s instructive to consider which identity aspects are being touted as “innate essences” and which aren’t, for example; and to wonder why, and what the political differences between these might be).
What would young people’s response be to the idea that any one of the following has an inner essence: race, social class, nationality, personality differences, what they like to eat, sexuality, religion, clothing choice, illnesses, liking for sports or not, melancholia, moral virtue, mental illness, promiscuity? At various points in history all of those have been considered to be, or not be, forms of “innate identities” or “innate essences”; and if some of them now look laughable it might be worth considering why we think our current understanding of these ideas might be so much better…?