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We recently got a national park near Oslo, Østmarka, it's kind of small though, and there are some power lines cutting through, and some forest roads and artificial dams, and large parts of it are quite affected by lumbering some decades ago. It's still nice though, but most of it is not pristine nature, and it's too small to just be wandering without encountering human infrastructure, or ending up outside of it.
The word national park also has really different meanings in different countries, so asking for it may not necessarily give the responses you are looking for. In Norway, national park is just a certain type of protection that's given to an area, it does not mean there's infrastructure for tourists there. It also has to be of a certain size, and it has to be of a higher standard when it comes to quality of nature and with no major infrastructure (these requirements were kind of skirted around when they made Østmarka).
In the map, it's the dark green area. It's not easy to walk to from the city centre, although possible if you have many hours, but you can reach the forested area by metro (then there's some walking in the forest to get to the national park).
