Pick a single small thing your team has been annoyed by and fix it fast. It buys more credibility than a strategy document nobody reads.
A strategy document earns you credit with your own manager. A fixed annoyance earns you credit with your team. In the first ninety days, you need the second kind more.
Step 1: Ask directly what's been annoying people
Not "what's broken strategically", "what's a small thing that's been bugging you." The answers are usually mundane and usually fixable fast.
Step 2: Pick the one with the shortest path to visible
Choose based on speed and visibility, not on which fix looks most impressive. A boring fix people actually feel beats an ambitious one still in progress three months later.
Step 3: Say you're doing it before you do it
Announcing the fix in advance means the team notices when it lands. A quiet fix gets a fraction of the credit of an announced one, for identical work.
Step 4: Name it again once it's done
Close the loop explicitly: "here's the thing you flagged, here's what changed." Don't assume people will connect the dots on their own.