If you are interested in this job, and they have actually looked at what you have made, and you want the job, just go ahead and take some interviews (remotely, you might not necessarily want to fly to NYC for an interview that doesn't pan out) and BE HONEST.
You're not going to do anyone any good by dishonestly "faking it till you make it". Companies don't assume that everyone knows everything when they get hired (so there will be time for you to "ramp up"), but you definitely want to make it known up front your actual level of expertise, and things that you know/don't know
2) Can you fake it? It depends. Some people have it easier than others when it comes to coding ... call it an innate capability. If you have "it" and can learn fast, you might be able to fake an entry level position without effort. Anything more, not so much I'm afraid. So .. have you ever coded before?
3) Seriously think it through if you're going to fake it. Apart from stuff like reputational harm, if you are an alpha-personality, you might find it very hard to fail badly at something. For instance, people stay in PhD programs for years because they are smart and have no idea how to fail out. If I were you, I'd be honest with them ... tell them the extent of your prior knowledge and experience. If they can deal with that and you can learn fast ... that's awesome. If not, no big deal, right? :)
So things can go two ways after they realist your true skillset:
1. They see your potential and offer you the job.
2. They turn you down but you get some solid interview experience.
Either way you have nothing to lose. I've mentored many different graduates and always tell them to take as many interviews as they can - even jobs they're not 100% interested in - because all that experience counts.
If you wanna chat more about this then feel free to shout me over at @modernprogrammr