Ostensibly, the United States is a meritocracy. At least, that's the aim. And there's some truth to it. If you're good at your job, you're more likely to get promoted--although people also sometimes "fail up." But no matter how hard you work, or how awesome you are at your job, you won't become a billionaire unless you meet one of these criteria. I'm setting aside the possibility of being born into it. That happens, but that just means someone else was a billionaire first, and they did one of the following.
You get one person to pay you $1 billion. This is a tough ask. You'd have to create something they really want. Realistically, the only way this happens is corruption. You can't legitimately produce something that one person is going to think is worth $1 billion unless you're doing something really shady. Maybe you become friends with a president of a corrupt country, and he gifts you the state's oil company. That's about it.
You get 100 people to pay you $10 million each. This will do it, but again, the numbers don't make much sense. What are the kinds of things you can produce that are worth $10 million, not just to one person, but to 100? Maybe you could be a world renowned artist, but very few artists in history have produced $1 billion worth of art, and the really valuable artworks gain their value after the artist dies. A Van Gogh is worth a lot in part because there will never be any more created. There's only one starry night, and always will only be at most one. That's what makes it so valuable.
You get 1 million people to pay you $1000 each. Or 10 million to pay you $100 each. Or 100 million to pay $10 each. In other words, you need a lot of people to pay you a bit of money. Realistically, this is the only way. You have to operate at scale. If I had to guess, I would say that close to 100% of billionaires have taken this approach. You run a company that sells products to millions of people, or you write a series of children's books read by the entire world, or you play a sport watched by hundreds of millions of people, or you con lots of people out of their retirement savings, or you gain control over a monopoly that everyone has to use. Scale is the key to becoming a billionaire.
What does this mean for meritocracy? It means being a billionaire is at best only very slightly related to merit. You could be the best sushi chef in the world, and run an extremely popular restaurant charging outrageous prices: $1000 a meal, for example. But that would mean to become a billionaire, even if we assume that $1000 is pure profit, which it won't be, you would need to prepare 1 million meals ($1000 * 1 million = $1 billion). If you cooked for 100 people a night, 365 days a year, it would take more than 27 years to earn $1 billion in revenue (again, not counting any of the costs of the food or waiters or rent or plates, etc.).
You could be the top lawyer in the world, representing wealthy clients and charging $5000 an hour. It would take you 200,000 hours of work to make $1 billion at that rate.
Any task you do for a small number of people will not make you a billionaire. You need to operate at scale. This is such a critical step to becoming a billionaire that I would say merit is only very orthogonally related to earning billions. And this doesn't look good for the idea that America is a meritocracy. Merit has some effect. You can live well by doing well. You can be a millionaire based purely on merit. But you can't be a billionaire just by doing well. You need to get a little from a lot of people, whether that's earned or taken.