My youngest is 12 and the SS number was filed for at the hospital following delivery. To claim kids as dependents you are supposed to list their SS numbers on your tax return so I doubt most people would wait until 12 or 16 years old.
That’s TODAY and 12 years ago ... it’s not 1977, well before the radical changes to SS that took place in the early 80s, and since.
Way back when, people (at least in large numbers) didn’t file false deductions for kids, there was a certain level of trust that no longer exists. Look up the SS regs in the 60’s and 70’s. Totally different from today.