PSU UP is only a no go if OP has not taken and is not taking Precalculus. Even in that case, if OP wanted PSU UP, they could take one semester of College Algebra in the Spring and report it on their STARS (SRAR).
If OP has taken or is taking Precalc (or equivalent), PSU UP would be a reach, reachable if they check “summer” on their application.
SUNY New Paltz, SUNY Buffalo State, and Alfred State are all fantastic ideas!