You can drive from Lindesnes, the southernmost point, to North Cape, the northernmost point in Norway, without ever leaving Norway, yes:

Due to Norway’s complicated geography it is far from the quickest route, however:

Counterintuitively the route through Sweden and Finland saves you 5 hours and is a little shorter. This is partially because Norway “spoons” Sweden and Finland, and partially because Norway is just one long mountain range, chopped up by fjords. This makes road building very difficult.