I mean, it should be absolutely obvious that not everyone has a gender identity.
Does a newborn baby have a gender identity? What about an unborn baby?
What about a child born so severely disabled that they have never been able to communicate?
What about a child raised in complete isolation who never develops the capacity for language?
What about someone in a persistent vegetative state who no longer has any brain activity?
I would argue that none of these people can be said to have a gender identity, and yet we would have no trouble identifying them as a boy, girl, man or woman according to their sex and whether they are pre or post puberty.
Obviously the majority of us are influenced by gender norms from a young age, but does that mean we all have a gender identity?
If so, how does someone who was born and raised male, is sexually attracted to women, fathered children, transitioned in middle age, has long hair and likes to wear dresses, makeup and high heels have the same gender identity as someone who was born and raised female, is sexually attracted to men, gave birth to children, has short hair and never wears dresses, makeup or high heels? What on earth are they supposed to have in common?