Some states allow print-outs of SSN (you can obtain a print-out two days after you applied for SSN at the social security office). However, IL requires the physical SSN card and do not accept print outs. In IL, it takes 14 business days for the SSN to arrive in the mail.

In the meantime, gather all necessary documents that you will need at the DMV and read the "rules of the road" brochure to be ready for the driving and written tests.