Was the California of the 1960s what makes it the "true Golden State" or were there other periods where California prospered?
As this is a "History" question, I expect that going back in history is acceptable. The first thing I thought of (which made it a "true golden state") was the California Gold Rush, which began in 1849.
Though Americans may imagine homesteaders deserting their farms and adventurers crossing the country to find gold, it might surprise one to know that people arrived from all over the world as well. (Eventually "foreigners" would be driven out, and Native Americans would be driven from their lands.) It is not hard to imagine the dreams of wealth that brought so many to California when...
...[a]t first, the gold nuggets could be picked up off the ground.
In terms of the prosperity the gold rush brought, consider San Francisco.
While one might think that California's draw would induce railroad companies to build routes to California, the opposite was true. California advanced so dramatically with the gold rush that it built a rail line to the country's eastern coast.
Originally California was a part of the Mexican Territory, but was signed over to the U.S. in 1847 at the end of the Mexican-American War. California quickly became a state by 1850—tied to the Compromise of 1850 (a group of bills put into place to ease tensions between "the slave states in the South and free states of the North," specifically to address territories won at the end of the war in 1847). Other towns in California popped up, growing at an amazing rate. Ranches were built to raise cattle, and the number of farms also grew, so as to feed the countless settlers arriving each day to "strike it rich."
In terms of growth...
It is estimated that approximately 90,000 people arrived in California in 1849—about half by land and half by sea.
While California has known prosperity during other times in the history of the United States, the gold rush had perhaps an unequaled effect on the state of California, and how it was perceived:
California's name became indelibly connected with the Gold Rush, and fast success in a new world became known as the "California Dream."
While some of us may think of the Mamas and the Papas, and their hit "California Dreamin'" as a song of the 1960s (1965-66), "California Dream" actually hearkens back to the California Gold Rush of 1849—referring to a time of affluence that changed the face of the West coast...and American prosperity as well.