California public universities generally do not use recommendations.
UCB does ask some applicants to send optional recommendations after they apply, though it sounds like these are commonly reused from recommendations written for other college applications if other colleges were applied to.
Yes, the student considering colleges that use recommendations should approach teachers now, if getting recommendations is a free-for-all. Some teachers get overloaded with requests and may refuse if asked later on. If the school has some sort of procedure for requesting recommendations (in order to distribute them and avoid overloading any particular teacher), find out early how this is done and don’t miss deadlines. Occasionally, there are threads from students complaining about recommendation rationing.