I'm pretty sure you have to go through an FFL.
Please correct me if I'm wrong.
FAQ at California DOJ
Q:. What is the process for purchasing a firearm in California?
A: All firearms purchases and transfers, including private party transactions and sales at gun shows, must be made through a licensed dealer under the Dealer Record of Sale (DROS) process. California imposes a 10-day waiting period before a firearm can be released to a buyer or transferee. A person must be at least 18 years of age to purchase a rifle or shotgun. To buy a handgun, a person must be at least 21 years of age, and either 1) possess an HSC plus successfully complete a safety demonstration with the handgun being purchased or 2) qualify for an HSC exemption.
As part of the DROS process, the buyer must present "clear evidence of identity and age" which is defined as a valid, non-expired California Driver's License or Identification Card issued by the Department of Motor Vehicles. A military identification accompanied by permanent duty station orders indicating a posting in California is also acceptable.
If the buyer is not a U.S. Citizen, then he or she is required to demonstrate that he or she is legally within the United States by providing to the firearms dealer with documentation that contains his/her Alien Registration Number or I-94 Number.
Purchasers of handguns are also required to provide proof of California residency, such as a utility bill, residential lease, property deed, or government-issued identification (other than a drivers license or other DMV-issued identification).
(PC Section 12071)