For all the problems everyone has mentioned about NJ, they do provide an easy to follow flow chart for the needed documents and allow you to reuse the step 1 and 2 documents for step 3 reducing how many documents are needed.
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Someone 18+ already with a NJ non REAL ID license could get by with only 4 total documents. Current license, bank statement, SS card, birth certificate. It doesn't say a marriage license is required to match the birth certificate but maybe that would be required as well if your name has changed. But those older might struggle to get a birth certificate.
For those under 18 it looks a little tougher to satisfy Step 1. Easiest path would be getting a checking or savings account and the statement from parents. They would at least be able to easily get a birth certificate, social security card, and waiver certificate from the school.