It is true that many members of the “Greatest Generation” who were born in the United States did NOT get a birth certificate issued to their parents when they were born (likely at home with a midwife present). If they needed one to enlist in the military, for example, they obtained one as a child/young adult by affidavit of a witness or attendant.
This generation’s numbers are dwindling every day and nearly 0% are still in the workforce. Many of its female members never held a paying job.