Agree with @thumper1 that it would be extremely difficult to establish residency in California for the California public colleges and universities (Private universities are another matter, but you still need cash for incidentals.) You would need to pay full fees at any public university because you would be coming to California for educational purposes, so, fees at the public colleges for nonresidents would be full fees without financial aid.
Working full time, for a year, to establish residency, would be extremely difficult because of the expense of just living day to day. Our public transportation in most of California is horrible. Finding a job that could sustain you, would be really difficult. You are not allowed any financial help, nor bartering system because that is not considered self-sustaining. You would need to maintain receipts that match your income to your California tax return. Many students try this, because they are so desperate to come to California, but their expenses do not match their tax returns, so they end up paying full fees anyway. California is now having a problem with homeless students because a number of students can’t afford rent and live in their cars or under bridges.
Besides the bed sheets and coats, you need cash for toiletries that you have to go through every month. Your roommate may or may not let you borrow their shampoo, laundry soap, or toothpaste every once in a while but that will only go so far, especially now in this Covid-aware environment. You also need cash for transportation if you plan on going outside of the University area. California is one of the most expensive states in which to go to school. Everything costs money, and it seems to be double in California.