It takes a tremendous amount of effort and time to drill an oil well. You have to do exploration, set up a.drilling rig and have established infrastructure. It would take 6 months to years to start drilling of the coast of California. This will do nothing for the price of crude oil.
From the article excerpt above:
Oil pumping operations are expected to begin imminently off the coast of California after President Trump issued an executive order Friday to resume oil drilling operations near Santa Barbara
It looks like you misread the article. It says PUMPING will resume, not drilling. They are already existing wells.