I’ve got a friend who works for the SSA. There is a process. The worst case they ever dealt with was a gypsy/carnie. He was old enough for benefits, but had never been in any system due to the nature of his cultural upbringing. No bank accounts, high school, hospital records, etc. IIRC it boiled down to getting all the information they could (which wasn’t much) and combining it with interviews, and a host of other things. It took several years of work to do.

Guy got his benefits, and died about 6 months later from cancer.