You're not starting at JFK. You're flying into JFK.
What airline are you flying into JFK?
Do you have TSA Precheck?
I'm guessing you are flying on 2 separate tickets? So you are not protected if you miss your flight.
Neos flies out ofTerminal 1. It is for international flights only. That means you have to catch the airtrain between terminals. That is outside security.
You are going to have to walk from your arriving plane to the airtrain, take the airtrain to terminal 1, go through security, and then walk to your Neos flight in 45 minutes to be onboard 30 minutes before departure.
I wouldn't take that bet with odds in my favor.
My suggestion is to get an earlier flight into JFK. Or be ready to buy a new ticket to Italy.