I think from this context it means: after (the thing that happened) - The team did great at the end of the game. - After the divorce, she was well. I know I’m not a teacher but I hope this helps!

1) The team came first/did better than the others. 2) Recovered from

It means exactly what the words "come" and "out" mean. There is no need for interpretation. To "come out" of a house usually means to walk out of the front or back door, but it could mean climbing out of a window or even up a chimney if you are Santa Claus. To "come out" of a divorce means to emerge from a divorce process, a painful thing that involves lawyers and legal documents. Once that process is complete, you come out of it either better or worse off. The sentence "the experienced team..." might be confusing because it does not state what the team came out of. That is left to your imagination. Presumably there was some sort of tournament and the more experienced team came out of the tournament on top.