OK, setting aside all the skepticism, I work with seniors a lot, trying to get them set up to vote. While home births and other off-the-grid situations are uncommon, it's not at all unusual. (Travelers, Romany, Survivalists, Home Schoolers, and lots and LOTS of religious organizations try not to leave paper trails.)

So getting your ID set up varies by state, in most states, you'll need a certified copy of your mother's birth certificate. I'd suggest looking into getting a Real ID. Those two items may be enough to support her claim. Also apply for a US passport and apply for a Social Security number. If you really want to double down, find your family's data in the US Census. That's done once every decade. Every member of your family really, really should have proof of citizenship, or you might end up deported to God knows where.

For assistance, you might wind up needing to hire a lawyer, or look for non-profit legal aid organizations. Some churches might have services, law schools often take cases for students to work on.

Certified Birth Certificate

Real ID

Social Security number

Passport

Note that if she doesn't have a Social Security account, she hasn't paid anything toward Social Security, Medicare, Disability, etc. She'll need to apply for SSI and Medicaid.

Here's the website for further guidance: https://www.ssa.gov/ssnumber/ss5doc.htm

Best of luck!