Maybe I'm wrong about this but it seems odd for a company to hire externally for engineering manager except in extremely rare cases? From experience in a few companies I can't think of people who were hired directly to that role (e.g. a people manager of engineers). I basically only see external ICs and senior engineering leader hires and internal promotion of engineers to engineering managers.
In my experience, when you start with a team of great engineers who all love to build it's surprisingly rare that one of them wants to stop building and start managing. I'd actually say most of the time, by which I mean more than 50% of the time, an engineering manager is hired rather than promoted. Obviously this is anecdotal.
>internal promotion of engineers to engineering managers
That assumes you have ICs who want to and have the skills to go into management. Promoting people for the sake of filling a chair leads to really bad dynamics.
Moreover, newly promoted managers lack experience and if all you have is the blind leading he blind then it tends to create issues. You need some seasoned people in the mix to provide guidance.
I think it's tricky to hire managers externally, because it's a hard skill to measure -- you can't really manage on a whiteboard. But, side-grading ICs to management isn't always ideal, so you should be open to hiring managers externally.