My experience has been that jumping from employee to any level of executive is the absolute hardest step, at least for me. I think once you are a team lead and have some number of direct reports, you can then start jumping your way up that ladder. But going from 0 to 5 direct reports has often seemed impossible. I'd be open to tips on how to do it.
You can see this on the IC track as well for top-tier tech companies - there is a step-function difference in mindset at certain levels.
Jumping from IC to line manager, as you suggest, is one; you need to recognize you are no longer shipping code but are shipping your team - they are your output, and their performance is how you are measured.
At director it switches again, you are responsible not precisely for the people but for your organization as a whole. There is an adage that you know you're a director after your first re-org and are moving people's names around as cells on a spreadsheet.
It changes again at VP, as an executive of the company you are responsible and accountable for an entire function. Excuses cease to matter, even external forces - you should have accounted for them. You are optimizing for the company's overall future and not your org or people.
This is a vastly simplified explanation, obviously.