I'm thinking the best option would be for me to focus on a few key projects that I can get my head around but I'd appreciate any advice from people who have been in my position.
I'm replacing a manager who has great knowledge of internal systems and business history. I don't have that.
Your priority will be helping the team achieve goals, shielding them from business chaos, and removing blockers. As another comment mentioned, you'll need to become a people person, listen, understand, and empathise.
As with everything in life, it takes time and practice.
One tip: Do not overthink it, and don't burn out quickly. Always allocate time for yourself, otherwise you'll hate the role.
You were picked for the role. You’ve got the qualities needed. Just work hard to learn the information now which specializes to that role and trust that you’ve got this.
0. Everyone feels like an imposter, especially in the beginning. I'm sure when you were an intern/junior, you felt like an imposter and got over it by continuing to do the thing.
1. Unless your company culture is toxic, I'd also tell your manager that this is your first managing role and you'd love their advice and ask them to fill in your knowledge gaps.
Being vulnerable like that at work might not feel great, but it's way better than needing to remedy something you messed up because you put on a facade that you know everything.
3. It's totally fine to ask your team about things you don't understand. "How did you do this when Ben was the manager? What worked about it? What didn't?"
4. One of the biggest changes from IC to manager is that it's a lot more difficult to fix things with more effort.
Say you're worried about delivering something late. As an engineer, you can work a late night or two and deliver on time. As a manager, it's much harder to fix issues by deploying more of your own time to them.
This is effectively leverage: Things can go very well without much of your input. But when things are going badly, you also can't fix it with just your own time.
Think about it like you used to be rowing a boat and now you're captaining a small crew sailing vessel: There's a crew that can go further, faster, but it requires working well together.
A) Becoming a people manager. This is easily underestimated. Your job is to ensure your team works in the company's best interest. That also means that the team stays a team, and is motivated. It means building a relationship with all team members. Everyone will be at a different place.
B) Understanding your area of responsibility, i.e. product, business, processes, and systems. This seems to be your greatest concern. Understand that by working with the team (area A) the team can handle situations where your own knowledge is lacking. It also helps to "intern" on topics by following something like an onboarding plan for yourself, that you define together with the team. Avoid becoming a micro manager, except when it is 100% clear the team is messing things up on a topic.
In general, I'd advise to be humble and transparent, and don't overpromise or overcommit to your team members.
Good luck :)