They knew how to work together. They did.
Clint and Natasha had worked together for years.
Tony and Steve repaired the engine.
Tony, Steve and Natasha had taken Loki down in Germany. Even if it doesn't seem like it, there was a lot of teamwork there, especially on Tony's part.
He didn't kill anyone, so you and your doubts can leave.
Tony and Bruce found the Tesseract.
Thor and Tony worked together when taking Loki down - again! - even though they... had their differences.
They really, really could work together. It could happen.
However, there were fucking aliens coming out of a portal in the sky holy shit, so there were some tough conditions for them to get it through their heads that they had to work together.
Clint, the one avenger that hadn't been introduced to the rest, was surprisingly sarcastic and dry humor in a way that both Tony and Bruce could get behind.
Hulk and Thor ... weren't exactly a match made in - what - Valhalla.
Steve and Tony still clashed - was anything else expected? - but Natasha and Bruce seemed to make up pretty fast.
It was surprisingly easy to work together from the moment they all collectively decided that, in Thor's words, they were being petty and needed to ward off an alien invasion.
That's not to say that the fucking warding off of said invasion was easy, because all of them have never had to do something so terribly, horrifyingly hard before.
But they worked together.
And it got done.
And they ate shawarma together, too.
They're not so bad at this team bonding shit, huh?