My first two kids, born 1980 and 1984, had to apply after Kemp-Roth in 1986 required SSNs for dependent exemptions. My other five kids had them issued at birth.
Issue at birth has been normal since 1990, at the latest.
I think I might have been 15 or 16 when I got mine. My wife and I are about the same age, and we both grew up in Philadelphia. My SS number starts with 175 and hers with 185, and the next two digits of each are the same. So clearly our numbers follow some pattern. I assume they would identify us (correctly) as having been issued our cards in Pennsylvania, and perhaps specifically in Philadelphia.