Documents for H4 Emergency Appointment

I’ll be starting a new job on 11/16/20. Can my wife go for an emergency appointment with my Offer letter and my previous company’s pay stubs? Or do you recommend we wait till I get my first paystub at my new job?

It does not really matter. She can attend using your current job or new job’s pay stubs.
The key documents are
I-94, your visa copy, your approval notice for h1B, your employment letter and then your pay stubs.
Check below experiences article