FLUSHING, N.Y.—Before Steven Slater, a 47-year-old stay-at-home dad, tried out for a part-time job this summer, he had to get ready. He added miles to his runs. He started doing yoga three times a week. Then he went to a park near his apartment in Manhattan and threw tennis balls against a wall.

At this year’s U.S. Open, Mr. Slater is a rookie ball person, a job that requires a rocket arm. The Open is the only one of the four Grand Slam tennis tournaments where the people who fetch balls between points also throw them to each other, rather than roll them.

That is part of the reason why so many of the ball boys and girls at the U.S. Open are adults.

“Baseball is not as popular as it was when I was growing up,” Mr. Slater said. “It’s more of a soccer generation.”

This year, though, grown-ups like Mr. Slater are more valuable than ever because Labor Day, part of the tournament’s traditional middle weekend, is late and the young arms have to go back to school, some earlier than usual in anticipation of snow days.