Bay Area Truck Routes
The main east-west routes into the Bay Area are I80, I580, and Highway 152. Highway 12 is decent 'back road' alternate, but Highway 4 is really too narrow for safety.
For crossing the Sierra mountains, I80 and Highway 50 are it. All the other passes are steep, narrow, and curving. Heck, on the east side of the pass, Highway 4 gets down to one lane switchbacks.