Final answer:
California's biggest problem after becoming a state in 1850 was ongoing conflicts with Native Americans, exacerbated by rapid population growth due to the Gold Rush and the national debate over slavery.
Step-by-step explanation:
The biggest problem California faced after becoming a state in 1850 was ongoing conflicts with Native Americans. After the discovery of gold in 1848, the population surged with the influx of "forty-niners" seeking their fortune, leading to a push for a rapid transition to statehood. Upon statehood, California grappled with political instability, especially the contentious issue of whether it would be a free or slave state. This heightened tensions between the North and South, further straining the delicate balance within the United States on the brink of civil war. While issues like economic growth and political representation were prominent, the struggle and conflict with Native Americans over land and resources became California's most pressing challenge, exacerbating the turmoil during these formative years.