Can I enter Beijing when on transit on my way home? I have 10 hours between flights. (norwegian)

I was wondering if I could enter Beijing when I arrive, because I have 10 hours there before email next flight, and would like to not spend them all in the airport. I checked the list of countries of approved 72hour free transit, and Norway is not on the list. So my question would be if there is any way I could pay for a visa of some sort allowing me to to leave the airport for a few hours?