Hello there
Regarding the SSN — we initially planned to get it along with the EAD, so we didn’t apply for it right after my arrival. However, after we got married, we changed our minds and decided to get my SSN earlier.
From what I understand, as long as you haven’t filed your AOS yet, you’re still allowed to apply for a Social Security Number - as long as your I-94 is still valid and hasn’t expired.
I first submitted my application online and then scheduled an appointment. On the day of the appointment, I brought my passport, our marriage certificate, and my most recent I-94. I received my SSN card just 4 days later!