I just got my daughter’s birth certificate from California and there you had to be the person, or their mother, father, sibling, child, spouse for starters. The rest were public official type that could get the certified copy.
Doubt if his sister would do it so I doubt if there is anyone else that could get the certificate.
Easy, just walk into the hospital and ask for his birth certificate. Tell them you're his only white half-brother/sister.
If they ask for proof, just whip out your fake birth certificate modeled after his.