First off, see if you can make an appointment on the website, it'll save you a lot of time.
Secondly, you don't actually need proof of your new address.
Check it out here:
- Social Security number.
- Your valid out-of-state driver's license.
- Proof of your true full name.
- Proof of your birth date and legal presence.
- Driver License or Identification Card application (Form DL-44). This form cannot be downloaded as original signatures and a barcode are needed to meet legal requirements. You may request a DL-44 by calling (800) 777-0133, or pick one up in person from any DMV office.
- Payment to cover the $31 license fee. CA DMV Offices accept cash, checks, money orders and ATM/debit cards.
If you can scrounge up your original birth certificate, social security card, and passport you should be fine. (Bring the lease agreement anyway, though.)