I don't think it's even a case of 'Marvel did it this way so they must do it a different way.' I think it's simply a case of do it whatever way works best for them and the movie. That could be the Marvel approach, could be a different approach.
Either way, looking over their shoulder at Marvel, whether to imitate or to make a point of acting differently, seems to be the wrong way to go.
That's a good point.
Sure there is. In the JL movie you intro with the same scene, then intercut flashback scenes of Batman recruiting the other 4 heroes while they finish that battle. Then continue with the movie. It practically writes itself.
Why do you even need the flashbacks? As has been mentioned above, there's a long history of "gather the team" movies, and there are plenty of ways of introducing team members that don't require flashbacks to their origins or recruitment.
One way to do it might be the X-Men
approach, used not only in the first movie but in various animated adaptations as well, not to mention numerous other team stories such as Stargate Universe
or the movie 9
(which I just saw so it's fresh in my mind): Begin with one character being recruited to join a pre-existing team or group, and use that character as the audience surrogate, letting the viewers meet the characters and learn about the backstory along with the surrogate. In this case, maybe make Batman the viewpoint character as Superman tries to convince him to join the extant Justice League. Or maybe have Princess Diana come into the outside world, establish herself as a hero, and then get recruited into the League. Or focus on a young hero who's just gotten powers and begun fighting crime -- say, Flash or Cyborg -- and follow them through their induction into the League.