When is the best time to start talking with a recruiter to get paperwork started for commissioning in the Navy as an ER nurse?

I'd contact them now and get the ball rolling.

Early because the recruiter won't be the one handling you. It will be an Accessions Officer that works the nursing side. That's the one you'll build the relationship with. Start getting into shape as Navy nurses also take care of the Marines. Women were bought into that realm years ago. Consider the reserve side as well in looking at your total life options. Also be prepared for a different type of hospital politics.

The faster you start the process the sooner you will understand the requirements. Get hopping!