score:16
You only need a Social Security number for working and paying taxes. If you're not yet working, you don't yet need the number.
But you apply for the number, not your employer. If you're in the US in H-1B status, I believe you should be able to apply for the number now. If you're worried about not having one, just go down to the local social security office and get yours.
Upvote:7
Many years ago I entered the US on H-1B and managed to rent a flat, open a bank account and get telephone/cable service without applying for a SSN. Since I was being paid outside of the US still, I didn't actually need one for quite a while. Even when I got one, I still told companies that I didn't have a SSN as I didn't want to give it out unless absolutely necessary.
As Phoog says, you only truly need it when you start on the US payroll.