How long after the mexican american war did they discover gold in california?

The American-Mexican War ended on the 2nd of February 1848. While the first gold was discovered in California on 24th of January 1848

Hence, Gold was first discovered actually a week before the War had ended.

Explanation:

The Gold was discovered by James W. Marshall at Sutter's mill. The news spread like wildfire across the country and over 300,000 people came to California in order to make new riches.

This completely changed the demographics of California for years to come. The native population was completely destroyed and California soon became an important region and not just a far-flung territory.