My last few jobs I started with a listening tour. I talked to everyone who was relevant to the job and asked them:

- what is going well,

- what is not going well

-what do hope that I will fix

-what should I do

-what should I not do

I put those question in the agenda for the meeting invite so they could come prepared. Then we took the conversation from there.

I put it all into a google doc, then synthesized it into summary that hid the identities of the people who said it and used it as my guide for the first few months.

Great approach - I'd add a key one: "Who else should I talk to / who is (regardless of title) effectively responsible for X?"