You can get to be a staff level engineer doing that. However, beware that to really make it up the corporate ladder, you actually have to reject that. Note that I didn't say reject doing the things assigned. I mean reject it as in you figure out the things that they should be assigning and get those done instead.
There are lots of different routes via staff and above level engineer. However, what they do have in common is working on really hard problems that take a lot of other people to work with. You will typically find your staff and higher level engineers rarely are actually writing code themselves. They are all management, but it's a technical management part.
The thing is, it's really hard to be there because management will constantly assign you various product-focused things and you end up being a widget. And so you have to figure out how to break out of that to say, no, this is the wrong widget and you have to show them that, look, I delivered this widget and when they see it, they should realize, wait, this guy was right. I assigned the wrong widget and he did it and so I need to trust this guy and give him more time to do things that give us the right widget.
Remember, the real goal is to make money for the company. As an engineer, you might say your salary is, say, $200,000 a year. But that is only a small part of it. For every dollar they spend on you, they need to spend $10 on other things to make it work. To pay your salary, you need to make not just enough product to bring enough to pay for your salary. You also have to pay for marketing, sales, product support, other managers, HR, and a bunch of other things I can't even think of off the top of my head. So the real question you should be asking is how do I earn, by actions I do, more than $2 million a year for my company. If you're earning your company $2 million a year as an engineer, they're breaking even on you at best, you should do widgets they trust will work. If they are earning $10 million, that's something that you should be putting on your resume and saying, look, this is why you need to give me a promotion. I am earning this $10 million every year. If you want to do even better than that, make it not $10 million that you're personally doing, but things that, because you're assigning other people to do them, are earning hundreds of millions. If you can earn the company hundreds of millions of dollars a year, you can justify a large salary for yourself, and you keep dozens of other engineers busy doing things.
Or you can take the lazy way out and just be a widget producing what they need you to do. That's good enough.