It would require capturing a zygote.

Did you mean capturing a gamete? As in, a viable sperm cell or egg? Which proves that the individual is biologically capable of producing those gametes, which means they are capable of producing viable offspring?

Because capturing a zygote (a viable egg that has been successfully fertilized by a viable sperm cell, but hasn’t yet implanted itself on the uterine wall to become an embryo) would require a woman to have a fertilized egg. And I feel like requiring impregnation just to confirm sex is a little… Impractical?

It would mean positively identifying males would be impossible, because they’re not capable of carrying a zygote at all. That that’s before we even get into the whole “in order to confirm an elementary school girl is biologically female so she can compete, the doctor would first need to impregnate her to create a zygote” thing.