No problem. First of all, you will need a document proving the citizenship.
Have you NOT established your child's U.S. citizenship with us before?
Yes, I haven't done that yet.
In that case we need to see proof of U.S. citizenship. We can accept only certain documents as proof of U.S. citizenship. These include a U.S. birth certificate or U.S. passport.
What if I'm not a U.S. citizen?
Well, then Social Security will ask to see a current DHS document. A  I-551 Permanent Resident Card would be an acceptable document.
And what if I don't have such a document available?
We may then accept the child's state issued non-drivers identification card or an adoption decree.
Oh, so an adoption decree would also work?
Yes, that is correct.
Does Social Security require a proof of identity?