From what I heard, (not sure if this is true), usually scholarship comes with the offer. However, in my case, one month after I accepted the offer/ paid the 5000 dollar deposits, NYU gave me a 15000 annual scholarship. One thing I do know for sure, the scholarship is merit-based, which means that if your stats or DAT is higher or at least equal to mine, you will most likely get a scholarship. I think this is a reasonable way to estimate whether NYU will give you a scholarship in the future.
I can definitely help you with that. Feel free to message me for stats if you feel comfortable.