The first step to get promoted is to understand the promotion process of your current company, if they have a formal one. It took me one year to learn how promos work in my current company, and that was one whole year of progress lost.
Then if you really want to get promoted fast, you need to optimize to meet the promo criteria. Often that is in line with OP advice, sometimes it is against it. And above all, learn about scope, impact and visibility. Also learn about optics and politics. Sadly often promotions are not so much about your accomplishments, but how you present them and how people perceive them. The old advice of "work really hard and you will be rewarded" is moot if the right people don't know about it. Some people get promoted faster by doing less but promoting themselves harder and louder.
Even if you don't want to exactly game the system, it is still useful to know how it is played. For example, if you accomplish some extraordinary, spend a bit of effort letting higher ups know about it.