Not quite story mode but you can go into a private match by yourself and start the game as either Pred or Fireteam.
As the Predator you essentially get 15 minutes to run around killing NPCs. It’s not amazing but it’s better than the tutorial at least. Can get a lay out of each map down as well as practice with each new weapon you get.
You also get a decent amount of XP from this.
Happy hunting.