Clarify your mandate in week one
Ask your manager about the nearest deliverable, commitments to other departments, and the limits of your authority. In conversations with your team, ask what already works, where people most often wait for a decision, and which commitment to customers or colleagues is currently at risk.
Observe the work by mid-month
Join a meeting where the team assigns work and speak to an internal customer. In one illustrative case, the team delivers on time and the next department is still unhappy because it hears about changes too late. Check whether that is what happened in several recent handoffs.
Set a review date by month end
Tell the team what you heard and agree on one small change. For example, for two weeks assign someone to communicate each date change. Decide when you will hear from the departments that depend on your work. If you have your own assessment profile, use it to identify a colleague who can give feedback on how you show up as a manager.