In 1925, a thousand acres of the Palos Verdes Peninsula was set aside for the Southern Branch of the University of California. (The Northern, original branch, of course, was in Berkeley.)
Until 1922, the PV Peninsula was owned by one man, Frank Vanderlip, who had great plans for the area. He sold part of it--the part that would become Palos Verdes Estates and Miraleste--to real estate developer H. G. Lewis that year. The thousand acres that would have housed UCLA can be seen on the map as the area left open, right in the center. That area is now home to the Peninsula Shopping Center and the high school. (Maureen Megowen's history site has more details.)
Technically, the Southern Branch of the University of California already existed--as a Teachers College on Vermont, in Los Angeles. In September 1919, that school first opened for about 1500 students. But the Southern branch didn't have a permanent campus, and other cities--Palos Verdes, Fullerton, and Burbank--wanted to host the new school. Los Angeles wanted to keep it too, and thought it would fit nicely onto a 200-acre parcel in Westwood. Turns out they were right.
(this is the Vermont campus)
The Southern Branch (on Vermont) handed out 28 Bachelor of Education degrees in 1923--its first graduates. That same year, the first African American sorority was chartered: Delta Sigma Theta. An African American fraternity followed: Kappa Alpha Psi. That location became Los Angeles City College.
According to UCLA History, boosters for a Westwood location--called the Beverly site--exerted a massive effort to pass Proposition 2, a bond measure that would raise 70% of the needed funds to purchase the site. Leading up to voting day, May 5, 1925, students used the radio airwaves to promote their cause (radio had only been around for 5 years, but everybody had one by 1925). They even produced a 10-minute film to be shown in local theaters!
This is Westwood in the 1930s--the campus is surrounded by farmland.
Needless to say (but I'll say it anyway) the proposition/bond passed and the Beverly site reaped the benefit. The campus was dedicated in 1930.