Your ancestor did have social security numbers.
Have you already requested his SS-5Form? Costs $27 but it should have his place of birth and parents names.
Name: Charles Trimbath
State of Issue: Pennsylvania
Date of Birth: Tuesday December 31, 1895
Date of Death: January 1987
Est. Age at Death: 91 years
You might want to check into an intent & petition. Possible he was naturalized.