How to buy a car with a new Social Security number and credit from scratch?

I want to make clear I don't have two SS, I've just got my residency through my husband and my brand new debt power (SS#) we need an extra car but his credit is already tied up with one car and our house, so how can I buy another car by myself using my ZERO credit score?? any idea? I have 3K for down payment and I go to graduate school but without student loans... we want a Mitsubishi lancer