Unfortunately, I think the fan idea is unlikely to work very well. When you exhaust the hot air in the apartment, that creates a negative pressure, which pulls air in from elsewhere. Where is that air going to come from? Outside. Where the air temperature is hot. See the problem?
I lived in a second-floor apartment in the south bay for several years. Even with a small wall-mounted AC unit, it was close to unbearable, because most of the construction around there involved uninsulated walls and roofs, and single-pane windows. As a result, despite the relatively mild climate, the buildings overheat from solar gain. A month in and you'll be practically dying, trust me.
You could buy multiple window AC units. They're not that expensive (to buy, running them is another matter...). Unless your apartment has no hallways, a single unit is unlikely to work well since it has no air distribution ability, so rooms far away from where it's located will still be hot. You'll probably need one unit for the living area and another for your bedroom.
Another option is a window swamp cooler. Swamp coolers are not as common in the bay area but can work very, very well. In the summer, the afternoon relative humidity in Sunnyvale drops to 30% at an 80 degree outside air temperature. At a pressure of 30 inches of mercury, we can calculate the wet-bulb temperature as 60.41 degrees. And a good 90% efficient swamp cooler will produce air very close to that. It'll be blowing air that's about 62 degrees.
Here is the formula for how much a swamp cooler can cool the air:
cooled air temp = outside air temp - ((outside air temp - wet bulb temp) * efficiency
You'll only need one swamp cooler, since it blows the cold air through the apartment, with you directing the flow by opening faraway windows. So you could put in a window in your living area, open a window in your bedroom, and the cool air will blow through both the living room and the bedroom, cooling down both rooms.
Bonus: swamp coolers are dramatically cheaper to run than air conditioners. Mine uses 200 watts of power and cools my entire house to 73 degrees when it's 95 and sunny outside. My south bay apartment's pitiful AC unit used 1.5 kW of power and still couldn't get the job done, and my bedroom was always incredibly hot. I slept in the living room during much of the summer.
If I could go back in time and tell my former self what I know now, I would definitely have installed a window swamp cooler. It would have made an enormous difference compared to that terrible AC unit. The south bay area is definitely a climate that can support them.