When, if at all, does initiative pass between players?
It does not ever change hands. Initiative stays with whichever player had it at the start of the game. It's not really mentioned in the "starting to play" book, but the Rules Reference is pretty explicit:


  Initiative
  
  Initiative determines which player acts first during the
  Ship Phase and Squadron Phase. It is assigned to a player
  during the “Determine Initiative” step of setup. That
  player is the first player and takes the initiative token. His
  opponent is the second player.
  
  •   The first player retains initiative for the entire game.