OP here is dodging questions. I'm in and out as fast as I came.
@Boiler and @Crazy Cat there are some states that apparently, issue DL and DL insurance to illegals. I think that is why Latinos prefer Florida. I'm not sure if the rules have since changed due to the new law. I think NJ too.
OP dad may be having ITIN and not SSN.
Funny enough, he may also be actually having SSN because back then, some states used to issue unrestricted SSN to F-1 students. Those were the lucky days. I came across someone who came on B-2 back in early 2000's and has one. She's just AOSing right now based on marriage to USC. All this time, she's been working at big companies using that SSN. I also know some F-1 students who got that unrestricted SSN from back in the days in some states. Nonetheless, both these 2 loopholes have since been sealed.