It is very easy to get to the beach from UCLA. You can take the Big Blue Bus to the beach in about 30 minutes tops, and it costs only 50¢. Alternately, you could catch the Metro Rapid in Westwood and get there in 15-20 minutes. It’s even easier to get to Santa Monica if you live on the Expo Line, which a lot of students do since Culver City, Palms, and Sawtelle are some of the only relatively affordable places left in west LA. Additionally, UCLA has a deal with UberPool that caps prices for students traveling from campus at only $6 if a fare is up to $15 (any cost over $15 is added to the $6 flat rate).
FWIW I’ve lived in LA for 7 years and never needed a car.