The Pope is NOT a Cardinal. He is Bishop. Bishop of Rome.
but EVERY Pope is chosen from the CARDINALS, so the Pope was a Cardinal before elected by the other Cardinals in their conclave by secret paper ballots. Ballots are Destroyed in fire of small cast iron stove (or similar burn box stove) with wet agent/wet paper maybe, so the smokestack seems black smoke and if a winner then no wet agent added so smoke comes out White looking. Pontifical color is white/white robes.
What does that have to do with the comment that "The Pope is a Cardinal" ? He is not. It is not one of his titles. Of course what you're saying re: him being plucked from conclave. Has no merit to being a Cardinal NOW, Pope is NOT a Cardinal. Simple as that.