I'm not saying its the most important thing or specific to the first days. But getting the dynamics early on will benefit you, your project and the people involved.
Also more specific to day one: have fun and be excited :) good luck!
Pausing and engaging on the benefits of a proposal can be incredibly valuable, even if your mind has already raced to the considerations about implementation and opportunity cost. Many engineers understand that there's no higher praise than a leader diving into the weeds on something, but many other stakeholders don't have the same context!
I suggest the opposite: assume good intent from everyone, listen a lot, don’t be afraid to ask dumb questions, identify people who can help your team and identify people who need your help. In leadership, the job is not about you, it’s about setting up your team for success.
The most difficult and political people I know think like this. They never see themselves as the problem. They just think they’re playing defense and playing the meta-game better than others.
If you go into a workplace thinking that your first step is to identify your enemies so you can be on constant high alert to defend yourself, there’s a high risk that you’re going to become the political problem you claim to want to avoid.
What if there are no enemies? What if nobody was denied this role, because it was added headcount to expand the team? Imagine the OP going in on the defense because HN told them to “identify your enemies” as the first step, but really their team just wants to add another person to the group? This type of advice causes more problems than it solves.
It's probably also worth figuring out who holds power and authority. It's not always based on org or chart.