There is no nationwide index of births - each parish has it's own records so you'd need to know WHERE the birth happened.
Sometimes you might actually have a small clue that you don't recognize as important. You could offer the info you have and see if one of us here who is practiced in searching Norway might be able to find the right location for you.
Or you could use the indexes at Familysearch.org
They are building free online indexes of Norwegian records - not complete yet but growing all the time.
If you find the WHERE in Norway we can help you here or teach you how to do it yourself.