I am Certified International Property Specialist and have done several transactions for international buyers, but not licensed to service you in NY.
Yes, you can get a loan, but you will need a larger down payment, and documentation. Use a Realtor and a lender who have experience and contacts in this segment, as it will make the process much smoother.
The Realtors who post on your Thread who work the NY area here will be a good source for potential reperesentation. And, of course, good input and advice can come from others who traveled the same road that you did. You have a good starting point with some of the individuals below.
About CIPS - Certified International Property Specialists - There is a member search link, here also.