Is there a way to lookup online all flights that departed from a given gate at a given airport on a given day (say, today)? For example, suppose I would like to know which flights departed from gate 28 at SJC this morning.
A significant part of gates get reassigned all day long, for various reasons. Also, many airports keep international departure gates intentionally unpublished, for security reasons; only cleared passengers of those flights can see them on the monitors inside the international area.
So looking at that for the future is probably 1 in 3 wrong or inaccessible; looking at it for the past probably correct but useless. I am not aware if this is published anywhere; you could try to search on flightaware.com or similar websites.
The flight status page of the airport gives you some data on gate usage: https://www.flysanjose.com/flight-status However, it's only a 4 hour rolling window and there is no history.
For many airports this information is available online but for only a limited period. The format that this information is in also makes it extremely time-consuming to use and only worth the effort in extreme cases.
I'm talking about recordings of Air Traffic Control ("ATC") services that are available on sites like liveatc.net. Generally speaking, departing aircraft will have to call ATC on the relevant ground frequency to request permission to push-back and start their taxi. In these radio requests, the pilot would normally inform ATC of their gate (or stand) number. Hence, by listening to the recordings of the relevant frequency, you could piece together a list of flights that departed from any given gate.
If trying to do this, one thing to watch out for is that, at some airports the numbering of the gates that passengers see is different from the numbering used for aircraft movements. e.g. passenger Gate A10 at London Heathrow Terminal 5 is used for busing passengers to aircraft parked on remote (i.e. non-airbridge) stands with numbers 570+.
For your example, liveatc.net has its page on SJC here and their archives of the Ground frequency here. You can pick any date/time in the last 30 days to listen to. (To save yourself listening to hours of silence, do note that times are in UTC not PDT!)