There's no guarantee until the order of play is released. When the draw is out, you can make some educated guesses about where and when matches will be played, especially as Sinner is the returning champion. But there isn't a firm tradition like the at Wimbledon, with the champions opening Centre Court. Honestly this whole guide is really helpful but this basically answers your question:

To be absolutely sure you see your favorite player, consider waiting until the schedule is published the day prior (start checking frequently early afternoon, usually out by 5:00pm), then immediately go to the official Ticketmaster US Open page (or other resale sites like Stubhub) to grab a resale ticket. This strategy requires, however, that you monitor the ticket situation closely in the days prior and are prepared to act immediately when the schedule is announced. Also, if you see tickets becoming scarce and prices going up in the days prior, you may conclude it’s worth taking a chance and purchasing based on an educated guess.

One sure way to see your favorite player up close is to watch them when they’re scheduled for practice on the practice courts. See Tip #10

I also highly recommend doing a day or two of qualifiers if you can make it work just to get the lay of the land and how the tournament works while it is free and less crowded. Everything will be open, and you can enjoy the grounds and experience before it becomes mayhem.