I believe it is very possible without a Mexican-American War. Colonists stream in following the Gold Rush, Mexico attempts to assert control on the mining industry, this causes unrest and eventually revolution. You might even have the Reform War start sooner without the MAW, which would make it very easy for Californian revolutionaries to secede. A USA that refused to annex Texas and start a war with Mexico is probably a USA that would be hesitant to absorb California, though there will be interest. By this point the California Republic could be establishing its own national identity, making favorable deals with Britain and France and using gold-rush money to fund the creation of a strong central government.
What is interesting is that an independent California that gains independence through revolutionary activity against Mexico might not include all of OTL US Southwest... the revolutionaries would probably only be able to hold their own in the California Goldfield region. You might see them demand territorially only the land that they have settled as well as the trails that connect them with the USA. They could make a deal with the Mormons in the Great Basin to help support the creation of a new state. Even so, they might draw a border at the Colorado River... the Californians and Mormons aren't going to want OTL Arizona or New Mexico which the Mexicans could probably hold easily.
The idea of the Latter-Day Saints proposing a united front with the Californians could be very interesting... I wonder what kind of government they would consent to cooperating in. They might decide to create their own nation-state if their objectives grow too different from those of California.