I don’t think the CUNY system provides much financial aid (beyond student loans) for OOS students.
Start by running the net price calculator (NPC) here: https://portal0.uapc.cuny.edu/uapc/public/fin_aid/financial_aid_estimator/FinAidEstimator.jsp
Have you completed your FAFSA? You will need your FAFSA EFC for the NPC. If you haven’t completed it, you should do that ASAP. Meanwhile, you can complete the fafsa4caster here: https://fafsa.ed.gov/spa/fafsa4c/#/landing
Is the NPC COA estimate affordable? Continue to follow up with the financial aid office. Providing FA information after May 1 is unacceptable, so continue to ask for the info.
Good luck.