Yeah, the forest is just random. Whether you find coconuts, bananas, mushrooms, the stream (where you can refill empty water bottles), animal battles, or stepping on a snake and taking unavoidable damage, it's all just random dice rolls which you get. Except for leaving, which is always just going back (clicking bottom of the screen) a few times.
Don't know if it's been changed in 0.4, but in 0.3 it was actually impossible to stockpile food. This is because whenever you find a coconut/banana tree in the forest, there's not multiple of them, there's just one of each. And when you take bananas, it takes 4 days to regrow (every time you find a banana tree after that there will be no bananas on them, until the 4 day counter finishes). Coconuts take 3 days to regrow. Even if you absolutely minmax (by making sure you have space for all the food whenever it's ready), you'll run out of food on day 48. And you can extend that by just a few days if you exploit the knowledge that you can store the chips and water you have on you at the start in the storage container that you shouldn't yet know exists (freeing up some extra inventory slots for gathered food on day 1).
My advice is to cheat and edit the food/water variables in the console.