While SSN is issued at birth now, it used to be applied for once you needed it, typically mid-teen to late teenage years:

"In August 1987, SSA began a three-state pilot of the "Enumeration at Birth" ( EAB ) process in which the parent of a newborn can request an SSN as part of the state's birth registration process. Additional states began to participate in EAB in July 1988."

So, it's possible she never had one.