Um, why would you post this inquiry in the Japan forum? You might want to alert a Moderator and request that this thread be moved to the FT New York City forum.
To answer your question, it's certainly possible to drive from Central/Southern NJ to JFK, but it will not always be fast. You would probably want to take the Outerbridge Crossing or Goethals Bridge to Staten Island, and then the Verrazano to Brooklyn.