Are you sure?
SSA has administrative offices that deal with data errors. Generally in a GSA high rise in a big city. NOT the offices where you go to get benefits.
Someone doing data entry for the SSA fat fingered some info about me back when I was born, and I only found out in the 2010s thanks to the IRS rejecting a tax filing (I had to pay a 50 cent late fee!!!).
Went in-person to their office in the Metcalfe Federal Building in Chicago and the lady spent a few minutes examining documents, typed on her computer for about 20 seconds, and that was that. All fixed.