Back when? I got mine when I was 9 in 1973.
Correct,...you got a SS# when you applied for it. There was not usually a need for it till you started working, but you could get one at any time. I always thought it was from where you applied, that is why you can identify the state with the first 3 digits. I hadn't ever heard of any anomalies about getting a number from another state. Kinda defeats the purpose of having state identifiers. I never understood why there wasn't a big kerfuffle when it became mandatory to get one at birth. You know we have been fighting getting a "mark of the beast" number for decades. Any type of universal identifier should have caused a ruckus, but didn't in this case. We all just fell into line an obeyed the gubmint.
I knew a guy that didn't have a SS# and was about 50. What a life he led. It was almost impossible for him to live, but he wouldn't take a SS# for religious reasons. Worked for cash, lived with friends and relatives, ect. That was 20 years ago. He's probably drawing SSI now on the dole. Either that or ole Beelzebub done put his mark on him.