Look at the case of Alecia Pennington in Texas.
Born at home, midwife didn’t file birth certificate, homeschooled, and when she went to apply for driving license, get a job, and go to college, couldn’t do anything because she couldn’t prove she was born here.
She also probably wasn’t issued a social security number.
7 of my kids were born at home. They didn’t get a birth certificate at all, but at some point we did obtain a document from the state of Indiana (I don’t remember the name) so they could go on a cruise. People who say “you have to have this or that” usually don’t know what the hell they are talking about.