"CityTicket is a new way to travel on Saturday and Sunday within the city limits on Long Island Rail Road or Metro-North Railroad. Your ride will be fast, comfortable, and convenient, and the cost is only $3.00 for single-direction one-way travel.
You can also use CityTicket on weekends to speed your trip to or from JFK Airport. Use CityTicket for Long Island Rail Road travel to or from Jamaica Station for your AirTrain connection."
Lots of trains running at 6am
5:28 arr 5:29
6:06 arr 6:29
6:11 arr 6:23
6:16 arr 6:37
6:37 arr 6:59
figure on another 20 minutes once you get on the AirTrain to get to your terminal