H4 & EAD together

I am on Day 1 CPT with an expired F1 visa and getting married in a couple of months to my spouse who is in H1. Her GC process has just been started. Can I apply for H4 & EAD together once her I-140 is approved? What’s the timeline to apply for H4 EAD once her I140 is approved?

You can immediately apply for H4/EAD once her I-140 is approved.

Can I get H4 EAD approved here and then go for the stamping?

Yes, guessing you have plan to travel so you will be going for stamping? Otherwise it is not needed.