It seems to me, that once they have their basic shelter built and some wood stocked in, they have lots of time where they do very little to keep from burning calories. I would think sitting and watching for animals might be a good use of time.
Yes, by far the best times to hunt are twilight and night, but with a traditional bow, I am not sure why you think this would be a bad time for them to hunt?
Why would the producers edit out any large animal kills? To be PC? They show plenty of killing and gutting of fish and flattening mice. I don't think they have made any kills.
Admittidly, the produces did them no favors as the deer in the area are protected, the mice have disease, and out side of a fox and some pig sign, not much in the way of small game. Still, I might be way off, but I believe I could use the bow to get food.