Or I have an idea,

All of them are sent out on a mission by their mentor, unknown to all of them that they'd run into each other. Maybe a small group of robots or something. They go to take them down but when they run into each other it throws them off, so they start bickering but someone speaks the voice of reason and decides they need to work together, so once the JLA sees they do well, they ponder forming the team again I guess?