Dart is the only Briton in singles action on Wednesday, with Jack Draper, Katie Boulter and Dan Evans in the opposite side of the draw.
The doubles competitions begin in New York, with Britain’s Wimbledon champions Henry Patten and Finland’s Harri Heliovaara taking on French duo Sadio Doumbia and Manuel Guinard.
Neal Skupski joins Michael Venus of New Zealand against another French pairing of Hugo Gaston and Gregoire Jacq.
British women’s singles number one Katie Boulter teams up with Anna Kalinskaya of Russia to play China’s Wang Xinyu and Zheng Saisai.
Elsewhere, defending champions Coco Gauff and Novak Djokovic return to Arthur Ashe Stadium to headline the evening session, which begins at 00:00 BST on Thursday.
Third seed Gauff will continue her US Open “victory lap” against German veteran Tatjana Maria, the world number 99, in the second round.
That will be followed by Djokovic taking on fellow Serb Laslo Djere as he resumes his bid for a record 25th Grand Slam title.
Djokovic, 37, is still searching for a first major triumph this year, having won at least one every year since 2017.
Alexander Zverev, the men’s French Open runner-up, and women’s second seed Aryna Sabalenka are among the players in action on Louis Armstrong Stadium.
Wimbledon champion Barbora Krejcikova and Olympic gold medallist Qinwen Zheng both feature on Grandstand before men’s eighth seed Casper Ruud takes on French showman Gael Monfils.
Read More: US Open 2024: Harriet Dart faces Marta Kostyuk on Wednesday; Coco Gauff and Novak Djokovic
