Need SSN or military ID for father to give to NPRC for research to find military records. Joseph E. Rush, Olivette, MO, 1912-1981, burial in St. Louis County. Pls help

NPRC has tried to find military records for my father, Joseph E. Rush, but due to needing SSN or military ID number (which I do not have) cannot locate said records.  How do I find these numbers to provide to NPRC to continue their search?