after EAD, can we get SSN

Yes, she can. Applying for and receiving an SSN is not a violation of her H-4 status either, so she won't need AP to re-enter the US.
 
EAD helps for job only, not return to US

After EAD you can get SSN and she can work. Although this does not help you to return to US without AP. Please do noit leave US unless you have AP, if she starts working. Other wise her H4 is fine.
 
Just go to your local Social Security Office with your passport ,
I-94 , EAD, and some other supportive stuff and file for SSN#.You will get it in 2 - 3 weeks.

Ranjan
 
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