The last widespread snowfall down to near sea level in the San Francisco Bay Area was 47 years ago, on February 5, 1976. Granted, there have been a handful of occasions since with small pockets of cold air allowing for snow to get close to sea level, but nothing widespread. And the odds against it happening later this week are small, but not impossible. The most likely scenario will be snow accumulations in areas around the bay above 1000 to 2000 feet.
Historically, there have only been 11 days when snow has been recorded near sea level in downtown San Francisco, Twice on February 5th; in 887 and again in 1976. (https://www.ggweather.com/sf/snow.htm).
The 1976 event was spectacularly captured by the SF Chronicle in this photo by Art Frisch.
The meteorology on Feb 5, 1976, showed a cold front having moved south over the state during the overnight hours and supported by a very cold 500 mb low (5280m) west of Pt. Reyes. The 1000-500 mb thickness was 5221 meters.
The hourly observations that morning showed snow falling at San Francisco International Airport, and it may have been the last snow observation recorded at SFO, since it is unlikely to have been picked up by current automated sensors. [I remember this quite vividly as I had worked a midnight shift as an observer at SFO some of those snowy observations and then drove home to the East Bay through a winter wonderland.]
The setup for later this week shows a similar strength upper low farther offshore than in 1976, with a 5210m minima on Friday morning. But will the moisture synch up with the coldest air and at the right time of day? The odds right now look better for low-level snow south of the Bay Area.