[Giants]

wait, if we are including never ranked schools, then there are a number of other answers:
Delaware and Missouri state made their FBS debut this year so they have technically never been ranked.  There are a number of other recent moves to FBs who also haven’t been ranked.  

BC

Yep.  There are quite a few; however, the question which school has been unranked longer than any other school.  New Mexico’s unranked string goes back to 1931.

[Giants]

wait, if we are including never ranked schools, then there are a number of other answers:
Delaware and Missouri state made their FBS debut this year so they have technically never been ranked.  There are a number of other recent moves to FBs who also haven’t been ranked.  

BC

Yep.  There are quite a few; however, the question which school has been unranked longer than any other school.  New Mexico’s unranked string goes back to 1931.