The quickest way to speed run this game is:
1. Go to the bosses office and wait for the narrator to unlock the secret passage by himself
2. Restart your game until you start looking straight into the room with the two doors.
3. Beat the game as normal.
Note: I found it took a few tries just due to sometimes the Narrator for me wouldn't automatically open the secret passage instantly. If this happens for you it might take doing the run anyway and trying again to make it happen.