The California Secretary of State generally takes 3-4 weeks to process regularly filed corporation and limited liability company (LLC) formation documents, but due to the holidays and the usual heavy end-of-year and beginning-of-year filing volume, is currently operating on a 6-week plus schedule. The backlog will likely diminish by the end of February, after the wave of new corporations formed for the beginning of the year subsides. One can check the updated business entity processing times (and those for other filings, as well), here.
If standard processing times are inadequate, rush filing options are available; however, these must be weighed against the slightly increased legal fees and costs and substantial additional state filing fees. When possible, filing over the counter for a small additional fee in a regional office can speed turnaround time substantially. The Law Office of Jonas M. Grant PC regularly utilizes this method to speed its incorporations for clients.