To coach a travel soccer team in New Jersey, you must complete three courses:
The New Jersey "State Certificate" course for coaches (about 2-3 hours online, plus a 3 hour on-field session; costs about $60).
SafeSport Core Training (about 2-3 hours online; no cost).
CDC Concussion Training (about 1 hour online; no cost).
You'll also have to consent to a background check when you volunteer (you do not pay anything for this).
For the SafeSport and Concussion trainings, you'll get a certificate or an ID number that you'll have to upload or enter in your Volunteer profile on Lawrence Hamnett's site.
You'll need to sign up for some session of the NJYS State Certificate course, at https://www.njyouthsoccer.com/coaching-courses/ . There's an online portion and an on-field session.
The online portion may be either an online meeting you must attend (with your camera on), typically on a Thursday or Friday night, or it could be a self-study course you do at your convenience. The course you sign up for will indicate which it is.
The on-field session will be 3 hours with an instructor. Most on-field sessions ask for about 8-10 student coaches to volunteer as "players" during the session, and then choose 2 or 3 additional people from the class to act as coaches for those players and run through an example coaching session as part of the course. Most people who attend these on-field session dress as players, with soccer cleats and athletic wear, though this is not required.
You'll also turn in a written statement of your "Coaching Philosophy", probably after the sessions are over.
I suggest accessing the SafeSport training through U.S. Soccer. Start by registering for an account at http://learning.ussoccer.com/. Find the "Coaching Education" section, then under "Courses" select "Available Courses". Select the "Supplemental Courses" button instead of the "License Pathway" button near the top. "SafeSport" should be one of the things you can select from Supplemental Courses, and you'll find information on how to sign up for the training.
This training is available at https://www.cdc.gov/heads-up/training/youth-sports.html.