Okay so something I forgot is a lot of schools have vaccine requirements and he almost definitely wasn't vaccinated. (My school system appears wishy-washy on their policy here, saying that a student could be excluded, not that they will.)

Looking at homeless family rights that my school system informs people of: Homeless students can enroll in school, because of federal law that at least exists in our own universe, whether or not they have all their records available. Steven might have qualified at kindergarten age since he and his dad lived in a van (he also likely would have qualified for free or reduced lunch, in part for that reason).

Typically the school I work in requires, at minimum: birth certificate, proof of residency, court papers proving custody if a single parent, and immunization records. There are ways to sign papers to get out of half of these but they involve multiple meetings with multiple people.

My school doesn't have any public policy about undocumented persons but its resource page does cite a court case providing precedent for it being illegal to deny someone education for that reason.

All of this is dependent on the US having the same laws in SU as it does here, which it might well not if Pearl was excluded from certain federal acts that might have been capable of making her a citizen.