The first month sets the ceiling for everything after it. Move too fast and you build on a wrong map. Move too slow and you lose the window where people expect you to ask basic questions.
Week one is listening. I meet every team lead the program touches and ask the same three things: what are you on the hook for, what's blocking you, and what would you fix if you could. The patterns in those answers tell you more than any planning doc.
Week two I map the system. Not the org chart, the actual flow of work and data. Where does a change start, who has to touch it, where does it stall. The stalls are usually the program.
Weeks three and four I write the operating picture down and circulate it. Owners, dependencies, the real critical path, the risks no one had named out loud. This is the deliverable. If by day 30 the team agrees on what the program actually is, the job got easier. If they don't, that disagreement was the hidden problem all along.
The trap is the urge to show value by shipping something fast in week one. Resist it. The fastest way to lose credibility is to solve a problem nobody had while missing the one everybody felt.