I used to wrok for NS-LIJ until 2007 when I left NY.
It's like that old commercial - How do I get a job without experience, and how do I get experience without a job?
You'll have to do what the rest of us did - start your resume with an IFT company. Apply for FDNY EMS. Apply to every hospital you can. If you work for Transcare, you may be able to get in to their 911 division after paying your dues. When I left, most of the hospitals wanted at least six months NYC 911 experience before applying. Back in 2007, Jamaica Hosp. had an IFT division, so you could try starting there as well, and try to get into Jamaica, Brookdale, or Flushing's 911 dividsion.
You may have to become a medic before you'll get into a hospital. I did the NY Methodist program. They use (used?) MaMo, Presby, Transcare, and Jamaica units for rotations. You can netowork while you're in class. That and my NS-LIJ experience helped me get a per diem job there.
The squeaky wheel gets the grease. Find out where to apply for each hospital, and follow up with calls every few weeks. If you start work with a private, always keep a folder with updated resumes on the ambulance. You'll make contacts on the street, and they may offer to drop off a resume for you.
BTW, NS-LIJ is very militant. One of my two cousins that work there left, and one of my former medic partners just finished our fire academy back in Oct. Others are trying hard to leave. Just keep that in the back of your head. the upside for NS-LIJ? They have a thriving IFT business that has contracts with numerous MD offices. From what I'm told, they run quite a few emergencies out of these places. They call NS rather than 911. So, an IFT shift can be more like a 911 shift instead of a dailysis derby.
until then, it's a $10/hr IFT gig for you, unless you can land an ER Tech job. I would apply for those too.
BTW (again) if you want a good fire career, Fairfax County has an open enrollment period that ends on the 17th or 18th (can't recall). It doesn't open often. You could apply there, and if you get the call, you can work there in case FDNY doesn't come through. No age requirement, $50k/yr to start, 25 and out w/ a 2.8% multiplier, and a three year DROP.
Edit: Most employers don't care about volunteer experience, since it's not measurable, like a paid job is. For example, NS-LIJ had a five year volunteer = six month paid 911 experience conversion. The six months was the criteria at the time to qualify for 911 shifts, instead of having to do time in 100% IFT for a year before being cleared for 911.