The expression "Get your act together" means do the things necessary to accomplish what you want to accomplish. It tends to mean that things were not very controlled before that.
It can be an admonishment: Come on, guys, get your act together. We'll never win with you playing like that!
I just need to spend a couple minutes to get my act together and then I can leave (as I look at my papers, etc. all over my desk)>
I believe the "we got it together" in this case means that they had a hard time getting things going, and eventually they "got their act together" and accomplished their goal.
Student or Learner