I saw a preview from the upcoming set recently. In it, there was an objective Behind Enemy Lines.

Reaction: after an objective enters play. Look at the top card if an enemy objective or command deck. You may move that card to the bottom of the deck.

5 health and 1 resource.

My question would be, does that trigger on itself? And will it trigger while your revealing objectives at the begining of the game? My thought is yes, but I'd like some other opinions. It would be awesome to look at you opponents objectives at the beginning of the game.

Yes, it will trigger on itself. It can also trigger during the setup, but remember that objectives are flipped up (ie enter play) one at a time during setup and that all of the DS player's objectives are revealed and then the LS player's objectives.