Many aggressive Sheriffs will shoot on their first turn. They likely will not have a gun, so they will shoot either to their immediate left or right. Shooting the one to the immediate right can be devastating for that player. If they weren't dealt a card that allows them to avoid his attack, taking the hit summons all other players to shoot at him like a pack of bloodthirsty wolves. First blood is vicious. Even if you are the left player, getting shot at at the beginning of the game can be difficult as you haven't had times to build a good hand, and if you are an outlaw, neither have your team mates. How to deal with this situation?
I think one of the big things an Outlaw can do when he is shot so quickly is NOT to declare his role right away by shooting back at the Sheriff, but giving some time for his team mate(s) to prepare by shooting the player he is next to (or another player that is not the Sheriff who is in range). If you have a gun, it can be a good idea to shoot at a player that the Sheriff cannot reach, so that if you do shoot a team mate, they Sheriff cannot gang up on him. Why is this in general a good idea? The Sheriff knows that he has a Renegade/Deputies out there who he should not kill, and so by acting as they would to divert the Sheriff's suspicion (shooting other characters besides the Sheriff), the Sheriff could be convinced you are not a threat. This can work especially well if the Sheriff does not have a gun, since he will not be able to hit the player you shot at. Thus, even if you shot an ally, it is not as problematic as the Sheriff will not be joining arms with you yet. The aggressive Sheriff's only choices are then either to shoot the other player who is next to him, or wait for a gun. I think salvaging your life in the first round is very important for the Outlaws, so do what you can to convince the Sheriff he has made a mistake. This is crucial if your character is someone who packs fire power, like Slab or Willy.