This response is initially persuasive but the line of reasoning doesn’t hold in other cases. For example, let’s replace gender with sexuality:
No one could possibly know they were “born” with a sexual preference. By the time they’re old enough to have memories and conscious thought, they have already been socialized.
Now, we all agree that sexual preference is something you’re born with. Analogously, if we reject the idea that lack of knowledge of innate sexual preference implies sexuality is a social construct, then we should reject the argument that lack of knowledge of gender identity implies gender is a social construct.