Railway is started by a card. To get the card to appear you need to have a Persuasive of 175 and be a POSI of the second tier or higher (one of the four stat specialisations or Paramount Presence).
The Cave of the Nadir will be discovered when you completed the associated quest. Can’t remember, but I don’t think that is connected to POSI status. As I recall the quest is moved on by random card draws. Once the the quest is completed the cave will be a location you can visit from your base camp in the Forgotten Quarter. You will only be able to visit the place once a week, though, for reasons that will become clear once you’ve been there.