Unless there has been some change in the last few years, Social Security numbers are NOT issued at birth. You have to apply for a Social Security number. Most of us did this as teenagers when we graduated from cutting grass or babysitting into a job that required our employer to withhold Social Security.
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.