Hi,
Yes, you do need a green card or citizenship to get your license in NY state. But you can take all the exams and do your internship (if you get a sponsor, I assume), before you get your GC.
The physical GC is required, as I understand it, for the license.
If you have any questions, you should call to confirm with the NY State Boards of Pharmacy. You can get their number from the NABP website. They are quite helpful with queries.
HTH.
Diya