Serial number

The starting letter at the beginning of the serial number is irrelevant to the New/Replacement/Refurbished status. In older iPhones, the starting letter/number indicates the factory where it was manufactured. In newer models it is totally irrelevant, as Apple is using random serial numbers.

It is, and always has been the model number that indicates New/Replacement/Refurbished status.

M = New

N = Replacement

F = Refurbished

P = Personalized.

The N leading character generally indicates that this is a device that Apple gave a customer when doing so was more expedient or more cost efficient than repairing the customer's original device. At the time it was delivered to that repair customer, it was either factory new or the equivalent, though any warranty remainder clock continued from the time the original device was put into service.

Did you receive the box with the phone? Phones like this are shipped in thin boxes that are only thick enough to hold the phone, but have a label with the phone's pertinent information, just like the sticker on the bottom of the original phone's package.

In all likelihood, your phone has never been used. Quite often, a customer who cannot suffer a few days' down time while a broken iPhone is in the shop will opt to purchase a replacement phone immediately and sell the repaired (replaced) phone after it comes back from Apple. I have purchased two iPads from people who did this.

If everything works well, I recommend that you enjoy your purchase.