The easiest thing to do is to get a State ID. This can be easily done at a local MVD.
Another option would be to get a Driver License. Since you're from Australia*, you will need to get a car (either from a friend or rented) and take a computer and road test.
For either option, I recommend getting an ID valid for Federal Identification (air travel).
You will need the following documents for all options above:
- Passport with Visa
- Mail with your name and current address (for travel ID only)
Please wait at least 1 week after arriving to the US to apply. It takes some time for SEVIS to update. Plus, your adviser needs to check you in the system.
In regards to the need of a SSN, when I got my license a few years ago SSN was not needed. However, it seems that now the SSN is mandatory. If so, you have 2 options: Ask the DSO to issue you a SSN or provide the DMV with a Form SSA-L676, “Refusal to Process SSN Application.” secure.ssa.gov/apps10/poms.nsf/lnx/0100299020
*Check the list of countries with reciprocity here: https://www.azdot.gov/motor-vehicles/driver-services/Tests_Manuals_and_Driving_Schools/foreign-reciprocity