However, you really don't even need to do that. You could just drive across the NY border to a state with looser gun laws, buy one there, shave off the serial number, and bring it back to NY. You could also just steal a gun from one of the many Americans who already own one.
You can also legally buy an unfinished lower receiver in many states (the part of a gun that is typically serialized). Since it's technically unfinished, it doesn't require a serial number. Then you drill a few holes into it and assemble it with off the shelf, also un-serialized gun parts.