I live in NorCal and do some culinary foraging for fun. There's plenty, I mean people lived here before Europeans colonized. There's all kinds of native berries, blackberry, salmon berry, service berry, elderberry huckleberry. There are plenty of nuts, beaked hazelnuts, black walnut and the most plentiful are acorns.
And there's plenty of small game to hunt and trap. I don't see that Petrov did this, but I imagine if he was comfortable catching and eating a neighbors duck, he probably took a squirrel or two in his life. The natives would obviously fish, take all kinds of small game, even including rat.