To prove immigration status, there are some specific documents you need.
Are you trying to prove your child's U.S. immigration status?
Yes I am
We will need your child's current U.S. immigration document, like a I-551 Lawful Permanent Resident Card, Machine Readable Immigrant Visa, I-766 Employment Authorization Document, EAD, or a work permit.
What if you are not a U.S. citizen?
Then Social Security will want to see a current DHS document like a I-551 Permanent Resident Card.
What about taxes?
You can apply for an Individual Taxpayer ID number
Can you get benefits and services without a SSN?
Yes, you do not need a number to conduct business with a bank, register for school, apply for educational tests, obtain private health insurance, apply for school lunch programs, or apply for subsidized houses.
Can you use a number to work?
No, you can't use it to work.
What happens if I work?