After having his tournament opener against Andrea Guerrieri postponed until day four, de Minaur had to endure another two-hour rain delay before seeing off the Italian qualifier in straight sets.
Former champion Daniil Medvedev and American home hope Alex Michelsen were already safely through to round three before de Minaur even made it on court for his opening match.
But the world No.7 was offering no complaints after advancing with a 6-2 6-2 6-4 victory to set up a stoush with Dutchman Botic van de Zandschulp.
"These tournaments, it's all about adapting and that's the name of the game," he said.
"There's too much to play for to let something like this affect you, so I'm glad with the way I handled it. I'm glad I got in and out, played a relatively clean match and now I can focus on the next one."
In a clinical display, de Minaur broke Guerrieri twice in all three sets and only dropped serve once, when he was trying to close out the match at 5-2 in the third.
But New York's miserable weather has left the sixth seed facing a scheduling backlog and needing to win seven best-of-five-set matches in 12 days to lift the trophy.
The three-times quarter-finalist will need to be back on site on Thursday (Friday AEST) to face the 70th-ranked van de Zandschulp and again the following day if he wins again.
One of the fittest players on tour, de Minaur is backing his supreme conditioning as he faces the prospect of playing three matches in three days.
"It definitely helps to be able to get on the court, get off the court and in straight sets. Every little bit helps." he said.
"Now I'm moving onwards, I'll be ready for tomorrow. It should be a battle, a physical one."
De Minaur's opener was initially slated for The Grandstand before being shifted to court 7.
When he finally opened his campaign on Wednesday (Thursday AEST), he was sent to court 11.
He looked intent on making up for lost time, racing to a 6-2 4-2 lead in just 49 minutes before the heavens opened.
After scampering back to the locker room, de Minaur returned to wrap up victory in less than an hour.Â
The 27-year-old was unfazed about not playing on one of the show courts.
"Again, it's a little bit of adapting," he said.
"Because of the rain, there's nothing you can do about it. You've just got to get out there, play your tennis match and, ultimately, if you win enough matches, you're going to get out on the stadium court.
"So that's the mindset."
De Minaur's more immediate concern was playing consoling husband after seeing his new wife, English star Katie Boulter, crash out of the Open with a 6-1 6-0 second-round loss to Wimbledon runner-up Karolina Muchova.
"Of course it's difficult," he said.
"Ultimately, we've got each other's backs no matter what and we've always got one eye out on each other.
"Obviously it was a tough day for Katie and I had to do my best to just focus on my task ahead and get the job done in the best way possible, and I'm glad I was able to achieve that today."
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