Yes, please do apply ASAP!
No, you should apply now. Once you’re over 75 days of the 90 days, you can no longer apply for an SSN and will have to wait until either GC or EAD are approved. You don’t want to be stuck without an SSN for potentially months since SSN is used for so many things in the US. It will be in your maiden name - they will want to see a GC or EAD in the new married name in order to change the name. Once you get those down the line, head to the SSA office and apply for name change on the card.