no? gender is still a culturally/socially established concept, regardless of how common cis people are. Other cultures don’t treat gender the same was as we do, which is in itself strong evidence that gender is a social construct. This doesn’t mean gender IDENTITY is entirely external (read “The Sense of Gender Theory") but that gender STEREOTYPES and expectations are social conventions, not “natural" or biologically determined. That is what “gender is a social construct" means, it does not invalidate transness (or cisness for that matter).

Basically internal sense of gender is definitely innate, but external influences (“pink is for girls, blue is for boys") are culturally dictated.