When the customs agent at Kennedy International Airport stamped Jenifer Guzman Gonzalez’s Mexican passport on Monday, Ms. Guzman was too anxious to look at it.

Back at her family’s apartment in Sunset Park, Brooklyn, Ms. Guzman started crying as she flipped to Page 5.

“PAROLED,” read the blue-ink stamp from the United States Department of Homeland Security. On the line under the word “Purpose” was the acronym: “DACA.”

“I didn’t want to look at it until I got home to savor the moment,” she said.

Ms. Guzman came from Mexico to New York at age 4, arriving by night hidden in a van. Now 21 and a sophomore at Hunter College, she had joined 66 others covered by DACA, Deferred Action for Childhood Arrivals, on a six-day trip to her homeland organized by the City University of New York. The 2012 federal program allows young, undocumented immigrants to remain in the United States temporarily and work legally. It also enables them to apply to travel abroad for humanitarian, educational or employment reasons, and then re-enter the United States, a benefit known as “advance parole.”