I applied SSN the very next day of receiving EAD and got the it in 10 days. don't think it's necessary to wait.
Got my EAD 9/26, went to local SS office to get me SSN 9/28. Takes me about 10 mins to fill the form wait with a number and took another 2 mins to speak to the clerk. Clerk said, the SSN should arriving in 7-10 days.