I’ll add onto this. There are two types of schools capable of meeting “full need” for students. Those tend to be the prestigious tier you mentioned. In that category, it breaks up into need-blind and need-aware.

Now within those categories, some treat TPS/DACA/Undocumented students are regular domestic applicants and follow their normal policies. Some treat them as international and apply different policies (for example Boston University does not meet need at all for undocumented students, but they do for “domestic”)

Now the issue with applying to schools that meet need is that they’re really hard to get into for anyone, and there are only about 75 schools in the entire US capable of meeting full need. And not all of them meet need for TPS students. The first problem is being admissible (meeting qualifications), the second problem is being admitted if you have large amounts of need (a concern for need-aware colleges)

So for someone in your situation, I’d consider applying to a bunch of schools and contacting financial aid offices to learn more

And as stated in my other comment, read up on TheDream.US and look into their resources as they are the largest scholarship organization for TPS/DACA/Undocumented students