There are basically 2 ways of becoming a police officer in the US. What method to use depends, in California, on the specific department.
First the simplest. In California all the major departments you must be hired by a department first. They then send you to, at least, a basic police academy. (LAPD, SFPD, ETC all have their own much more extensive, and harde, academies) You graduate, take and pass the state certification, POST in California, test and you are a cop working for the department that hired you.
Second. in California you can “self sponsor”. That means you find a police academy, the POST commission publishes a list of approved schools, you apply, pay them, go through a basic academy, pass the POST test, get certified and go out trying to find a job. Not until hired by a department are you a cop.
LOts of departments use the LAPD academy but the curriculum is that of the basic academy,.
If hired by LAPD first you do not pay for the academy and you are paid while in training. If you do not make it you are out of a job.
Your LAPD time does not count as part of a basic academy if you decide to self sponer.
They period of time it takes to get onto an eligibility list for major departments like LAPD can last 6 to 12 months after the test.
Once eligible you have to wait for them to pick you for a class starting.
One suggestion. You DO NOT want to start your cop career in your own home small town or your own community. You need working and living as a cop experience before you try that.