Somehow the regular clock built into the phone knows what time it is... yet standby needs to start off in Cupertino? 🤨 That's some really goofy sh*t. Why wouldn't the default clock just start off as matching the present location of the phone or whatever location/zone the regular built-in clock is using?
Simply editing the default clock widget to change Cupertino to your city is the solution, albeit a bit clumsy at first. Press and hold the clock, enter passcode, then press the clock again, then tap on the city's name and type in new city.
Otherwise, that's just what I've always wanted on my nightstand, a clock showing the time at Apple HQ, which is several time-zones away. 🤣