Definitely build a cellar if you're in a spot you intend to settle. It doesn't take too long to make and helps a lot.
If you're near a village, trade the extra meat to them for food that keeps better. Like dried/smoked meat or fish, or veggies/grain. Or trade for some salt and salt the meat from your kill, that makes it last a lot longer. A village of any culture will have some longer lasting food around for trade. If you encounter a wandering hunter or woodsman they will occasionally have some, and even if they don't they usually know of a nearby village. Villages are everywhere, often you will even find vagabond or forester villages in between the main faction areas.
If you're trying to play without interaction with npcs as a challenge, then you just have to hunt more frequently until you get yourself a cellar and a smokehouse built.
It doesn't take that long to build a small smokehouse though - all you need is 54 logs and 8 boards to build a little shack with a 2x1 interior. Then 35 stones for the fireplace. That's probably 9-10 days to gather materials if you have a woodsman axe, probably more like 15 without one. Then you can build walls at a rate of around 1.5 a day with proper tools, probably more like 1 a day if you just have the woodsman axe. So another 6-10 days there. But that's focused on building, so only doable if you are eating from stockpiled food or living off catches from traps or nets. It's feasible to get one up within two months even with lots of hunting in between though, as long as you're finding good kills.
Also, settling near some hills or a mountain near where game wanders is useful. My current char is living near a river with hilly terrain next to the river. Often I can go up the hills and spot large game nearby, making finding them much easier. Then it's just a matter of tracking them until they wear out and going for the kill. Putting an arrow or javelin in them before they get away can make this step a lot easier since they don't go as fast or as far wounded.
Do you cook the fishies before you put them in the cellar, or do you go straight from the water to the cellar?
Cook food first unless you're about to be ready to smoke/dry it, since roasted lasts longer.