NJ and maternity leave

Does anyone live in NJ and understand how their maternity leave works?

I work at home and my company headquarters are out of state. My OB says in NJ you can go out at 36 weeks.

My work says they won’t approve anything before I give birth unless I’m having complications. This is a very large company. I have everything set up to get my 12 weeks after delivery (6 weeks if vaginal and then 6 weeks allowed fmla) but am tired and exhausted and want to go out at 37 weeks

Any insight would be much appreciated!