If you live in New Jersey, you must have a New Jersey driver’s license in order to drive a vehicle in the State of New Jersey, or other states.
The State of New Jersey Motor Vehicle Commission issues driver licenses. You can read additional information about driver license applications on the Department of Homeland Security U.S. Immigration and Customs Enforcement website.
The State of New Jersey Motor Vehicle Commission uses a 6 point ID verification system. One of the documents required is a Social Security Number (SSN). If you qualify for a SSN, you should obtain this first. If you do not have employment and therefore are not eligible for a SSN, you will still have to ask the Social Security Administration for a letter confirming they cannot give you a SSN. This letter is called Form SSA-L676.