For any player ranked outside of the world’s top 250, qualifying for the main draw of a major is a huge deal and Choinski will ultimately take satisfaction from his time in New York.
The prize money of £75,000 will also be useful as Germany-born Choinski looks to climb back up the rankings.
However, there will also be a sense of regret at not taking his chances to claim the second major win of his career.
Having switched allegiance to Great Britain in 2019, he reached a career-high ranking of 123rd last year but has struggled for consistency this season.
But the big server with an aggressive forehand played his way into a Grand Slam first round for the first time, having previously been given wildcards to play at Wimbledon.
Choinski – whose English mother and Polish father met while attending ballet dancing school in Germany – looked to maintain his rhythm against 55th-ranked Carballes Baena.
Trailing by two sets and a break, Choinski looked to be heading for a quick exit as Carballes Baena’s doggedness and ability to put lots of balls back from the baseline led him to make a flurry of wild unforced errors.
Suddenly, midway through the third set, the British player began to find his range with winners now outweighing the mistakes.
“When I went two sets down, I still felt I was hitting quite a good ball so I just had to face the situation and make the best out of it,” he said.
Demonstrating his physical and mental toughness, Choinski recovered from early breaks to win the third and fourth sets, levelling the match and forcing what had seemed an unlikely decider.
Carballes Baena left the court for an extended bathroom break, returning calmer and more composed as Choinski again became erratic on the way to losing in four hours and 31 minutes.
“There have been days where I have felt better than how I feel right now, especially fresher after that match in 32C [heat],” said Choinski.
“That puts some stress on the body, but I’ll survive.
“I was struggling in the past three days to get rid of the [cold] and get my body into a position where I could go for five sets.”