You're right, thank god US citizens aren't given a unique number at birth that they'd later need to attend school, get a driver's license, buy a house, or get a job.
Social Security Numbers are applied for voluntarily by the parents of the baby. Usually the hospital puts together the application from what I understand, but the parents can request that the hospital not do that. If a parent makes such a request, they usually have to educate the nurses that Social Security Numbers are not required by law, and are voluntary. If required for taxing purposes, a person without a Social Security Number will have to apply for an Individual Taxpayer Identification Number (ITIN). There is even a process to remove yourself from the Social Security program once you are 18, or convert to a religion that does not approve of it.
I would also venture to guess that not having a SSN or even an ITIN to use in place of the SNN is an automatic disqualification for attending school, getting a driver license, buying a house, or getting a job.
That's needed to verify unique identities when doing specific official business with institutions. It's not what's going to show up when you log into your work computer, send an email, use Facebook, or any of the thousands of places that computers use our names.
