I know a lot of singles who have adopted and it hasn’t been an issue on FAFSA. Even if they were once married, FAFSA views the student as having a single parent.
What can be an issue is if the adoption was international, the schools sometimes ask for proof of citizenship. This has happened even if the SSA has the student as a citizen. You then have to provide proof to the school, IN PERSON with original document (Certificate of citizenship or passport). I think this is happening less since many foreign adoptees have citizenship under the Child Citizenship Act and were issued SSNs after they had been granted citizenship, but the SSA is full of errors.
It didn’t happen to my daughter and there were never any problems in her status or admission even though she originally had a green card and I had to change her status at SSA, but it did happen to a lot of people I know.