carmen, you seem to think getting the "number" will be some cure-all.
You mention rent an cell phone:
well, for rent, if you submit your nimber, this is for credit and background check. When they run that number, since you are giving it to them before you are in the sytstem, they will recieve an 'empty' or worse 'fraudulent use' response. So they will come back to you asking, "what;s up with your SSN, show me your card", "Um, I don't have a card yet", "OK, bye" -
click
For the cell phone, they are running a credit check. You are a ZERO on the credit check, so will not be able to get anything without TALKING to someone, and explaining your situation. Giving them a nascent or virgin SSN doesn't help you at all. And not having a card in hand makes it WORSE.
the only 'advantage' of having number sooner, is that employer may start paying you sooner. If this sis not an issue for you, drop it.
Focus on developing your alternate methods of establishing your creditwortiness, like the Cdn report, etc, like others have said.
Your SSN card will come soon enough, you will get credit in the long run, and should be in debt up to your nose just about the time they lay you off....
So, as I said last week: What's the hurry?
