Zoe got the shot the first day she became eligible, on Aug. 2, and it was accompanied by a $100 gift certificate given as a vaccine incentive at the Barclays Center. (Her mother allowed her to spend it on anything she wanted.)

“The nurse was really excited about wishing me a happy birthday,” Zoe recalled.

Zoe’s mother, Nicole Tu, said she had told her daughter she could wait if she wanted. But, Zoe said: “I knew that was the quickest I could get it. I was excited because I could feel safer.”…

For some young people, getting vaccinated adds poignancy to a birthday. Many spent the past year isolated from friends, yearning for normalcy and confining their friendships primarily to phones and computers.