Canadian USMD on F1 matched into a program sponsoring J1

I am a fourth year med student at a USMD that recently matched (early match) at a program that sponsors J1 visas only. I am a Canadian currently on an F1 and was wondering how to proceed with switching over to a J1 while I am still finishing up my med school (graduate in June) to be able to get my on-boarding stuff in order before my July 1st start date. How do I go about getting a SSN in time for on-boarding? Do I have to wait until I switch from an F1 to J1? Thanks in advance.
Source: Student Doctor Network - Category: Universities & Medical Training Authors: Tags: Medical Students (MD) Source Type: forums