I assume that the players actually want their characters to get along, even if they grouse about it. That's genre-appropriate: even the characters who seem like fierce loners (I'm looking at you, Wolverine) have a reason to stick with the team. (If the players don't actually want to get along, you as GM should know that.)
I'm also going to assume that you as GM don't want to run each character solo until they join up with the team, or help create the team. That works, and I'm not knocking it. It's just not what I'm talking about.
What I'm talking about is an excuse for the group to be a team, right from the start.
One of the nice things you can do comes from Masks. Just ask them. Start with one and say, "Who were you fighting in your first adventure?" The next player, you ask, "You decided to stay with the team, but why?" And so on... But if you want rationales, here.
The Coincidental Threat
The equivalent to the tavern meeting is that everybody shows up to fight the evil of Quatragon, and at the end of it say, "Hey, we're pretty good as a team." A variation is that everyone is captured by the Subjugators and they need to work together to escape (and bring down the Subjugator ship while they're at it).
This is almost the same, except that the reason everyone shows up to fight the demon Quatragon or the alien Subjugators is that someone (PC or not) has foreseen that their group will do well together, and has made sure that they're in the right place.
The Common Origin
It's possible that the event that gave them superpowers affected everyone in the team: they were all together when the polymetabomb went off, or when the gas was released, or they all snuck aboard the experimental spaceship. A variation is that they're all family members, and the common event happened years ago, when mom and dad got exposed to the mutagenic material. Now all the kids have superpowers (and possibly spouses who married in and had superpowers anyway: why wouldn't someone who can bend steel want someone impervious as her spouse?).
Well, the superhero team is expanding (or being created), and they need new blood, so they've announced tryouts on Thursday, Friday, Saturday, and Sunday. There's a standard set of tests, and a set of group tests; identities are hidden until time X. If it's a government team, maybe there are requirements about eventually showing the identity; if it's a private team, maybe not. If it's a corporate team, maybe they have to sign away individual looks, so that plushies and dolls can be made. In both cases, somebody is funding the team: maybe it's an ex-hero who will act as a mentor, or a crazed billionaire who wants to have someone who will act on his whims. Either way, it's possible that the player characters have to leave the tryouts to deal with a real problem.
There are other ways to get folks together but those are the four easiest.