H1B and H4 EAD parallel processing

Hi All,

Need an information on next step.

My 2021 h1b is getting processed still, which may take couple of more weeks.
Meanwhile, my spouses i140 is approved and we wanted to apply for H4 EAD too.

Can we apply for H4 EAD in parallel with H1B?
If yes, i have another question.
In i765 form there is a question regarding SSN, saying whether i am applying for SSN or not? If i select NO , i have to provide my SSN which i don’t have. If i select YES , EAD may take 3 to 5 months and also i get SSN only then, but if my H1B is approved in next few weeks then i need SSN which i cant apply again as i already applied along with i140 and i can’t work for many months

Looking forward for suggestions and inputs on the next steps.

Thanks in Advance!! Appreciate your help!!