Historically, even cis people have asked these questions
What defines a woman or man in your opinion?
There's a great scene in Erin Brockovich where one of the clients asks "Are you technically still a woman if you have no boobs and no uterus?" because she's had them removed for medical reasons and Erin says something like "Of course. You're a happier woman because no Tampax or underwire bras."
Historically, men were MADE, not BORN. You had a right of passage of manhood and in some cultures if you didn't pass it, they put you in women's clothes and assigned you women's work.
See I'll make a man out of you in Mulan as evidence of this long-standing concept that men are MADE, not BORN.
Merely being born with a penis didn't give you male privilege and in my opinion the modern expectation that being born with a penis gives you male privilege without proving your manhood in some way -- ie your character, ethics, toughness and willingness to sacrifice for the good of society -- is a root cause of a lot of corruption and societal problems today.
My father and ex husband were both career military. I have long joked "If you served your country via military service, you're a manly man in my eyes. Even if you wear pink shirts, walk with a swish and have a boyfriend."
Yes, I've said that online years ago. It would be possible to prove that if you wanted to. It's probably on Cyburbia somewhere at least once. My handle was Michele Zone.
Some cultures also have tests of being a real woman, often rooted in giving birth. My north star is "I'm a good mom." Adoption is a thing and plenty of cis women have fertility problems, so that's not necessarily excluding anyone.
I rather like the plot point in the movie The Birdcage that the young man getting married and trying to fit into a conservative political family related to the bride ultimately says essentially "This gay man is my real mom." Because that's who raised him, not his biological mother.
I don't have answers for how trans people can validate "what gender I REALLY am." I can tell you confidently that historically even in extremely conservative heteronormative cultures that didn't want to acknowledge the LGBTQ crowd, defining "a man" was not "He was born with a PENIS. End of story."
I can also tell you I heard of the concept that "gender is a social construct " long before I heard of trans anything. I heard of it as a feminist or women's lib idea rooted in women trying to say essentially "Me not wanting to be your bitch and chattel property with no legal rights as a human being doesn't somehow make me less feminine or less of a woman. There's nothing whatsoever about being a woman that REQUIRES me to eat shit and LIKE it. You abusive mother fuckers are making that up because that works for you. That's a NO from me. And I'm still a woman, thanks. So kiss my fat ugly ass."
So for me and my purposes, my personal definition of trans is "sex hormone syndromes requiring MEDICAL care in the form of hormonal stuff to adequately support their health including immune function."
And you are all free to decide for yourselves how girly or manly you want to dress or whatever. Not my department and completely normal behavior for CIS people.
So you do you in that regard and I'm just going to sit over here and wonder about diet and supplements to address hormonal syndromes.