When would gold be discovered?
It might be quite a long time, actually. The whole discovery of gold at Sutter's Mill was a freak accident. Basically they made the tailrace portion (tailrace-a ditch that drained water away from the sawmill) of the sawmill they were building too narrow. James Marshall decided to use the natural force of the river to widen the tailrace/ditch. It was this activity which uncovered the gold...which would not have occurred if the tailrace had been constructed properly in the first place. There's not a lot of reason to suspect that the gold would have been found without that accident of poor construction occurring.
And if you look at the other discoveries of gold or silver in the West, they all were butterflies from the discovery of gold in California...people who accidently discovered gold while on the way overland to California, or people who had been inspired by the discovery in California, caught gold fever, and set off looking for their own discoveries. Take away the California gold discovery, and none of that happens.
Indeed, it would probably be the late 1890s, when gold was accidentally discovered in the Yukon, before there would be a major western gold rush. Once that occurs, people will start fanning out over the west looking for other veins.