Agree with all the advice that doing it internally will likely be easier (per the "When you're doing something new, don't do something new" maxim).

That said, changing companies can enable rapid evolution. It'll (potentially) make it easier to be the manager you want to be, as opposed to the manager they think you'll be. In many cases it's likely better to do it where you are, but wanted to advocate for the benefits of the alternative, it's not guaranteed to be worse.

My path involved switching to a combo IC & manager at a place where I was an experienced IC, but my skill as a manager didn't really develop until I switched companies.