I'm sure record of individuals feeling they are meant to be the opposite sex exists and may have been categorized as homosexuality.

Disclaimer - I am using modern terminology and the terminology of the time and try to distinguish and clarify as much as possible

As /u/tgjer refers to, Magnus Hirschfeld was actually one of the first people to distinguish between homosexuals (or urnings as they were often known at the time), transvestites (cross-dressers), intersex individuals, and what we would now refer to as non-binary and/or transgender people.

Magnus refers to all LGBTQI people as "sexual intermediaries" and still often conflates homosexuality and femininity (famously during the Eulenburg affair, he diagnoses a man as homosexual as he displays feminine behaviour, but distinguishes this from the act of sodomy), which caused conflict with other gay rights activists at the time.

He wrote Die Transvestiten, as far as I know the first study of transgender and transvestite people, in 1910.

It includes many case studies of people who presented as female while being assigned male at birth, or vice versa, as well as intersex individuals. This text distinguishes between what he refers to as "psychic transvestites" or " 'Geschlechtsuebergaenge'" (often translated as transsexuals and what we would now term transgender people) and "crossdressers".

In the 20s, the Hirschfeld institute provided (what we now term) gender affirmation procedures to those clients diagnosed as transsexuals, such as hormone therapy (implanting testicles or ovaries), oophorectomies, and mastectomies.

The institute also offered so-called adaptation therapy (sex-positive therapy to help people cope with their non-standard sexuality through self-acceptance) to all LGBTQI individuals.

Edit: removed some unimportant info and added exact wording