I don’t remember. My kids got their SS cards at birth, but how? Maybe it is something hospitals give you a form for?
That is one of the most telling things about the case of Barack Obama. He never had a legit SS number. From age 16-the presidency.
These days, hospitals have the parents sign the SS forms before the new family leaves. Not much to it. I didn’t do that with my first two, and got the stink-eye over it.