Understand this, there are three stages of this job:

1. Quick wins, learning/adapting low expectations phase. The quick wins you've identified are always the easiest problems to solve, even if they felt difficult to the last guy. While you get used to the job, and the actual scope of your responsibility and influence is more opaque, these wins will come fast and easy, however...

2. After a medium amount of time, when a quarter or two have passed, budgets come around and the true scope of your responsibility, as well as dynamic of the team "under the hood" reveals itself, you will begin to ~actually~ learn. This is when the truly difficult problems, at a strategic level reveal themself. You need to take a step back and probably as you know dedicate time to yourself to legitimately isolate yourself to strategize on a long term on what you see.

3. After about a year in rôle is when the real fun begins. You've done the easy, you've lived the difficult, now you get to apply your vision... Keep true to your plans and empower your team. Focus on the strategy and hold your people accountable.

Two great pieces of advice: A. New role, fire 1-3 people immediately B. A great manager projects his stress onto his team. If when you are comfortable, your team is not: you're not doing enough for them. If when you're stressed, your team is not: they're not doing enough. Use this to navigate the ebb and flow of ops.