You all are fortunate to be able to do so where you are. Unfortunately California is stuck in the past and after six plus years of regulatory petitions and appeals to try to get big bore airguns allowed in CA as method of take for wild pig, it is still a denial from the Fish and Game Commission on the request with adverse recommendations from the California Department of Fish and Wildlife.
With that said, despite California being stuck in the past on this issue, a significant number of other states have got hunting laws and regs on the books allowing for wild pig take with big bore airguns.
Edit: I've included sources to maps below that show what states we are currently allowed to hunt wild pig in with airguns.
For javelinas and / or wild boar, you can see regulations or laws allowing use of airguns (described in some states as BB devices) to hunt (boar, feral pig, or javelinas as defined) in (the states of) AZ, NM, TX, LA, AL, GA, SC, NC, and FL, and I think maybe one or two other states. (O.k, it is more states than that. But those are the easiest ones to find on the regulatory map.)
You can also review this state by state or by category such as "wild game" or "nuisance animal" at the following regulatory repository for airguns:
https://www.pyramydair.com/airgun-map/ Or, check the "states allowing use of airguns to hunt feral hog" comprehensive overview here:
https://www.pyramydair.com/airgun-map/?hunting=Big_Game#approved_Feral_Hogs As you will see there are a lot of states that allow this.
Note that in California, after a recent change in law on wild pigs, wild pig is being moved out of 'big game' to an 'exotic' category that gives wild pig less protections than before, but the Fish and Game Commission in CA still has not, and shows no signs of wanting to, adding method of take to allow use of big bore airguns on wild pig by hunters.