Where to Apply
There are two DMV offices nearby. The office closest to UCSB is the Goleta DMV office. The Santa Barbara DMV office is in downtown Santa Barbara.
DMV Social Security Number Exemption
If you are legally present in the U.S., but ineligible for an SSN, you are exempt from the DMV SSN requirement. You may start an application for a noncommercial driver license or ID card, and once your eligibility status is verified, the DMV will complete your application.
You must still provide an acceptable birth date/legal presence document for any future DL/ID card application or provide a valid SSN. You may not start an original CDL A, B, or C application until DMV visually verifies your SSN.
Read more about this on the CA DMV website here.