There are other ways to prove eligibility. For instance if you've been working for 50 or more years then you're likely to be eligible. Or you might have school or other records that give you an approximate age. Or your children may have birth certificates that give you a minimum age.

The real world is full of anomalies and missing data, the system deals with it according to the law and administrative precedent.

Edit: here you go: https://www.ssa.gov/help/iClaim_poa.html