The earliest possible discovery of gold within the OP's specified time frame is Sebastian Vizcaino's expedition, which got as far as OTL Monterrey. Apparently he wanted to found a settlement at that location IOTL, but his boss got sent to become Viceroy of Peru and the replacement was less supportive. Maybe a PoD would be Gaspar de Zuniga not getting sent to Peru, so the Monterrey settlement effort goes ahead and there's a Spanish presence in central California from the very early 1600s onward (some military justification: protecting the Acapulco Galleons from English raiding, since Drake had claimed the region shortly before?). It'll take a while to go from that to finding gold--IOTL, it took 80 years to go from the first Spanish missionary efforts to the discovery of gold, so they might not actually find any until the latter half of the seventeenth century--might California become contested during the War of the Spanish Succession?
Vizcaino's Wikipedia page also says that he was involved in diplomacy with the Shogunate in Japan at this time, and his own disregard for Japanese court etiquette helped sour relations. Perhaps if he's busy as Governor of Alta California at Monterrey, someone else has better luck maintaining relations between Spain and Japan--which could put Japan in an interesting position once gold is discovered and Spain stumbles into another great European war.