I'm a Northern NJ local.
Traffic will start to build to potential stop and go levels after about 6:30, be at its worst from about 7am to 8:30am, and ease up after 9am. If you can schedule the drive in to hit the Delaware River Bridge at about 9am, that will put you past the worst all the way to the NJ Turnpike Newark Bay Extension that is the way to Jersey City and Liberty Harbor. If this will be an afternoon trip, get yourself to Liberty Harbor by 3:30pm
As previously posted there is a toll on the Delaware River bridge, but not in the eastbound direction. The NJ Turnpike extention is tolled though.