The first question is what you want out of life, do you want to be manager, and executive, a technical lead or do you want to be purely technical? All four offer promotion paths at large and (increasingly) small companies although staying technical will hit an age issue eventually. They are also very different tracks.

That said, it sounds like you want to be an executive and let's say one at a larger company (ie: not a paper executive but an actual one). The skills you need for that are going to be leadership, management, charisma, politics, and networking. Since you're not going the technical track your technical skills are secondary at best.

You want a nice title on your resume so pick a top company and join there. Find a manager who is not afraid of your ambition (a career middle manager will likely be, find someone with ambition), act like a leader and get promoted. This will give you pedigree while also teaching you about politics and management. You will eventually hit diminishing returns.

Then, like the people you mentioned, jump to a startup as one of the founders or the person running it. This will teach you how to be a standalone leader, build up a network, and give you some executive-ish experience. It's vital you have the skills at this point to impress people at first impressions and maintain a networking relationship with them.

Then either get acquired by a larger company or switch after a while using your network to find the new position.

They are not that good, rising mainly due to timing and the political climate.