1. Chaos. At least in your head, but don't show it. First week is learning more about where you work than what you'll be doing.
2. Find out how things are done now, especially concerning support for the remote locations and the employees.
3. Ask for the diagram of the network - see what monitoring tools they have and get familiar. Look at the service history of the network and see what areas are problematic and get your skills together for that. Ask about policies and security - learn them all better than anyone else, and enforce them religiously.
4. You should get a feel for how "tight" a shop they run rather quickly. Understand what makes your boss(es) successful and be sure you are doing those things that will support their efforts. Always be ready to learn something new and NEVER turn down an opportunity - even if it's beyond your immediate scope, you can make your limitations known and still be offered opportunities to be involved in what's next and what's cool.
Be calm, cool and collected and watch what goes on, then insert yourself where you see a maximum benefit for you and your group - everyone loves it when everyone is successful. Your place in the pack will define itself.
And don't be a dinkus to your end users - remember, if they've had to reach out to you, their job is messed up because of "your" systems. A little grace under pressure goes light-years. You'd be surprised how many remote users with business-level responsibilities will drop your name - good or bad - to the people they work for.
Good luck!!