You don’t.
And no, I’m not saying “just quit” and walk away. If you’ve joined a team that is producing, hitting its targets, and generally getting along, you’ve actually stepped into a pretty good situation. The worst thing you can do is assume that because you are the new Project Manager, everything needs to change.
This is where I think a lot of PMs get themselves into trouble. They arrive with good intentions and start looking for things to fix. They introduce a new tracking system, add some ceremonies, change the meetings, create some new templates and generally start PM’ing the hell out of everyone.
The team hates it. The PM gets frustrated because nobody seems to appreciate all the wonderful process they have brought to the organization. Eventually everyone is annoyed with everyone else.
Instead, I think the first job is to stop trying to manage the team and start figuring out how to support them.
If they are already getting things done, let them get things done. Spend some time watching how they work and getting to know the people involved. Ask questions. Find out what frustrates them, where things get stuck and what they wish worked better. You may discover that the team doesn’t need much from you at all, or you may discover that there are some very obvious problems that nobody has had the time or authority to address.
That is where your value as a PM starts to show up.
Maybe you eventually introduce better tracking because nobody has a good view of what is actually happening. Maybe you change a meeting because everyone agrees it is a waste of time. Maybe you create a regular conversation around risks and decisions because things keep getting stuck for the same reason.
And yes, you might even introduce a meeting that everyone initially thinks is annoying.
But if it actually solves a problem they have, there is a pretty good chance they will eventually appreciate it.
The difference is that you didn’t walk in and decide what the team needed. You listened long enough for the team to show you.
A good PM doesn’t necessarily make a team more “process-driven.” Sometimes the best thing you can do is leave a team alone.
And when something does need to change, make sure there is a reason for it that matters to the people doing the work.
You aren’t there to prove that you are the PM.
You’re there to make the project, and the people working on it, a little easier to deal with.