That doesn’t logically follow. If he has a social security number he (or his parents) HAD a legal birth certificate at one time. It’s no guarantee that it still exists. I couldn’t produce my original birth certificate to save my life. I have the one I requested when I was 40 years old, which looks nothing like the original (which I used to enlist 20 years earlier).
You don’t need to be a citizen to have a social security number.