The answer to your question is that if she is looking to have a residential experience at SUNY it is 100% unlikely that she will receive enough money that she will only have to pay $2000 out of pocket.
As others have stated, each SUNY school has a net price calculator.
Here is the link to the TAP estimator
https://www.hesc.ny.gov/pay-for-college/financial-aid/types-of-financial-aid/grants/estimate-your-tap-award/tap-award-estimator.html
Even if student had a 0 EFC, package would look as follows:
Full Tap 5165
full Pell $6195
Loan $5500
SUNY Credit ~ $1500
total aid ~18,360 leaving a gap between 4-7k for a 4 year SUNY.
Regarding Excelsior, OP would not receive excelsior because Excelsior is a last payer that will kick in once TAP and Pell have been exhausted. There is also a huge drop off in how much money one will receive in TAP once EFC is above 0.
OP’s affordable option is a school where she can commute within the CUNY (if she is in NYC)/SUNY system as tuition and fees will be covered without having to take out loans.
Is family eligible for any of the NYS opportunity programs- EOP, HEOP, SEEK, College Discovery? Please remember opportunity programs ask for income/assets of both custodial and non-custodial parents.