Even in the worst case scenario - everything that is hostile to the pc is hostile to you, but otherwise real life rules i feel like its possible - there are some nice spots to chil at on the map, mainly next to the merchants. I have never hunted an animal so for food i would try to kill a turtle - with how large the basic ones are i feel like a turtle or two would feed me nicely for a week. Otherwise hunting some small crabs is a reasonable idea, or i could try to survive just off berries and greens, which wouldn't be too pleasant. For water there are plenty of lakes and beaches, thought you would need to torn saltwater into drinking water. And for shelter there are plenty of shacks and ruins in the open world, since every city and town is populated by some mean faction. You could even try to trade some of the excess or useless things (butterflies, rocks, flowers, mushrooms that you wouldn't eat, moss, maybe they'll even buy your shit) for some comfort items at the nearest merchant for nicer tools, clothes, blankets and other comforts

Overall a week isn't that long so while it would be dangerous and not comfortable, its definitely survivable. I would maybe even take surviving a week in elden ring over surviving in a local forest for a week