They can ship the firearm to an FFL in New York who will hold it until it until you get your permit and the gun is listed. All you need is the serial number to have it added to your permit.
You'll have to contact the county about the exact procedure because some counties allow you to submit the serial number with the permit application and have it added directly as soon as the permit is issued (in fact some require a firearm be purchased/listed/owned before a permit can be issued) while some counties will require the permit to be issued before a gun can be added.
In any case, it will have to be shipped to an FFL in New York in order for you to take possession.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.