Ohn, Eric, and Dying posted great information.
In short, it’s possible. People have done it before.
But it depends - what is your major? Regarding your 60 credits, you’ll need to take certain classes on top of general ed (IGETC or Breadth). If it’s in humanities, you’ll likely need less prereqs to apply into your desired major at the UC. If it’s STEM, it’s a bit tougher. My friends needed quite a bit of calculus/lab classes before getting into computer science.
You can check Assist.org to see which prerequisite classes you’ll need.
Other factors to consider include registration times. Is your local CC crowded? It could be tough to get into your classes when you’ve got a late registration time and a crowded CC. If you need CALC 1 and CALC 2 and you don’t get into CALC 1 for fall semester, that disrupts your schedule since you’ll need it to take CALC 2. Classes like that you’ll have to watch out for.
Also, some schools’ll be stricter than others. Some might not want 1-year transfers. I’d check with UCSD and UCLA’s transfer department. You could also make an appointment with your CC’s counselors (be warned though, some might suggest more more classes than you’ll need. Double check with Assist.org).
And if you do push for the 1 year CC route, look up professor ratings. 20 units is a hefty course load so you’ll want professors that might have a more forgiving curriculum. You’ll want good grades. 60 credits doesn’t guarantee you a place in a UC.