iirc, all I did was show the form from my high school driver’s ed course. No SSN. No birth certificate. For that matter, I don’t know if the high school form did anything. It was a year old before I got my license. The clerk at the SoS took one look at the form, laid it aside, and handed me a learner’s permit, as if I had not had driver’s ed at all. Of course, that was over 50 years ago. The US is orders of magnitude nuttier now.
Steve