The third-ranked woman from Britain, Dart, easily defeated Frenchwoman Chloe Paquet, 6-1, 6-2.
However, Choinski, who advanced to the main draw after winning three qualifying matches, fell to Spain’s Roberto Carballes Baena 6-2 6-3 5-7 6-7 (5-7) 6-3.
Too many careless blunders eventually cost the British men’s number 10, especially in the first two sets.
He will also regret not being able to convert five break points after leading 0–40 in the opening game of the championship set.
“Overall, I’m pleased with my performance in this match.”
I’m confident I can improve on this in the future,” Choinski stated, adding that throughout the illness he had struggled with a “full-blown cold and sinusitis.”
On Tuesday, Jack Draper, Katie Boulter, Emma Raducanu, and Dan Evans, four more British players, will play their first games.
Since former world number one Andy Murray retired at the Olympics last month, the US Open is the first major competition.
