Sorry to harsh on the OP, but why even try to mess with this? Get a passport. This birth certificate stuff seems like the kind of thing that, even if it's technically allowed, is going to be made a problem by some ignorant/obnoxious UA staff person. And so it was. And once you're in that jackpot any attempt to challenge his/her "authoritah" is going nowhere (other than the police station, if they feel "threatened").

My kids both had passports before they were four months old.