What do you mean by "what do they do in the wild"?
Baby guinea pigs are born fully furred, eyes open, ready to run, and will even begin to try and eat things on their own shortly after being born. No need for a nest for babies like that. Baby guinea pigs don't normally stray too far away from mum if let out in a large area.
You won't find straw in the wild, you would find whole grass plants leaves and all. It also doesn't tend to get very cold (or very hot) in the areas of south america guinea pigs are thought to originate from, but being fully furred even from birth guinea pigs do tend to cope better with cooler temperatures than warmer ones.