sometimes they will send you within a week or 2 after the EAD, sometimes they won't... if I was you I would booked an appointment at the SSA Office asap and when they will ask you if you ever received 1, you will say "NO". You will have your card in no less time.

i got my SSN first a week after approval, still waiting on my EAD (they havent sent it yet)

I got my EAD on Apr 25, still waiting on the SSN. I called and they said to give 7-10 business days before going to the local office

when I received my EAD based on DACA back in 2014, I went to the local social security office(I live in Cincinnati,Ohio) with my EAD and applied for one and recieved it in the mail about a week later. never was aware USCIS issues SSN and sent them to the applicant.