Learn to make one. It's not complicated. Get a sharp knife and hatchet, cut down a hatchet sapling, and cut off everything that isn't a bow. It won't be beautiful, but done right it can take small game.

Source: I make and sell bows. If you're seriously interested, contact me.

Look at survival guns. Do you want to actually survive, or larp as robin hood? I do shoot compound bows, thats how i hunt deer. Because the best area to hunt where i live is archery only after october. In an actual survival scenario my bows can go fuck themselves, guns are way better. You can only carry so much survival shit. Ill be carrying guns if shit gets real. Rational priorities.

All that said, im not saying you shouldnt get archery tackle. Its fun and is a good tool for hunting depending on where you live. But a bow aint what im grabbing if shtf.