The short answer is yes, a foreign author can appear on the NYT Bestseller List, but it's difficult, and I'm not sure why anyone would want to bother if that was their only goal.
If you want a career as a writer, statistically speaking you're better off self-publishing. You have to do all the work yourself or pay freelancers to do it for you, but you keep much more of the revenue, and you retain control over the book's rights and the direction of your career. You don't have to worry about the publisher dropping you because your last book didn't sell, or refusing to publish your new book because it's too different from what they think your readers expect from you.
The NYT Bestseller List is a list of (some of) the bestselling books that week in (some of) the bookshops in the USA. I'm fairly sure that their list of bookshops excludes amazon.com. So if you want to appear on the NYT list, you'd better plan on having your book on sale in American bricks-and-mortar bookshops. That means having it published by a big American publisher, and having the publisher give you a big advance. (The book won't get onto the NYT list without a lot of marketing. These days, publishers don't do much marketing for you unless they've given you a big advance. A big advance means they stand to lose a lot of money if the book doesn't sell. If they give you a small advance, they don't care if they lose that money, so it's up to you to do most of the marketing.)
To get your book published by a big American publisher, you'll probably need to have an American agent. In theory, all American agents accept books by foreign writers, but many of them won't be interested unless your book is something that would appeal to American readers and you've sold a lot of copies in your own country.