Until 1986[1] most Americans didn't get a Social Security Number until their first job.

In The Matrix (1999) there's a scene where Agent Smith explicitly remarks that Neo has an SSN as proof he's a law-abiding citizen in a white-collar job.

[1] when it was made a requirement to claim tax deductions for dependent children. Even today, if you don't want the tax break, you can opt out at the cost of ruining your child's life!