Actually, Social Security numbers were first issued in 1936 (after the Social Security Act was signed by FDR in 1935). I have several SS applications in my source documentation files from that timeframe.
This particular ancestor has been so elusive that finding an application for him might be really helpful. However, the last time I requested an application search the cost had gone up quite a bit. (I have no idea how much they run now.) So I'm reluctant to request it unless I have good reason to believe one exists.
Anyways... still curious if SSNs were required for non-citizens. Anyone???