Taveras, holding tightly to his gift, proudly affirmed that he knew about Mays and his neighborhood ties long before Friday.
He wasn't the only one excited to welcome Mays back to the neighborhood. Judging from the standing ovation the crowd of roughly 300 middle schoolers gave Mays, the moment wasn't lost on anyone.
After studying about the history of the Giants and the Polo Grounds in preparation for the visit, the students were a captive audience as they listened to Mays recount stories of his early playing days in the Negro Leagues and his transition to the Majors, on and off the field.
Sitting in front of an enlarged photo of himself playing stick ball with local children in the 1950s, the "Say Hey Kid" recounted stories of his routine with the kids.
"I used to have maybe 10 kids come to my window every morning," Mays said. "They'd come at 9 o'clock, knock on my window and wake me up, and I had to be out at 9:30 a.m. They'd give me a chance to take a shower and give me a chance to eat breakfast. But I had to be out there at 9:30, because that's when they wanted to play. I played with them for maybe an hour. ... There was a drugstore on the corner, and I used to go buy ice cream every day for them before day games."
The image of a young Mays playing with the neighborhood kids captured the day especially well for Giants president and COO Larry Baer, who was also on hand for the celebration.
"That's my favorite image in all of sports," Baer said. "It's such a return to an innocent time. You think about that, after a game or before a game, you're out by the ballpark playing ball with the kids. ... It was just such a beautiful time."
An introductory video took students back to that time, illustrating the iconic baseball events that took place in their own backyard, like "The Catch" and "The Shot Heard 'Round the World." After a brief interview with MLB Network analyst and former Major Leaguer Harold Reynolds, Mays took questions from the students ranging from his early life to his life after baseball. Along the way, Mays imparted some wisdom to the students about the importance of family and education.
Mays played the first five of his 22 seasons in New York. The team moved after the 1957 season. "The Catch" was in the 1954 World Series, the Giants' last World Series win before 2010.
Fifth-grader Justin Burke asked Mays about how he decided to play baseball over basketball and football.
"In baseball, I was getting $600 a month from [the] Birmingham [Barons]. [That] $600 was taking care of my family. ... Baseball was so easy for me, I had to pick baseball over football and basketball," Mays said. "You pick what you want to do to help your family. Your family comes first."
Mays highlighted family and education as two important pieces to reaching their dreams.
"Education is the key to this lifestyle now," Mays said. "You have to get an education. ... I say go as far as you can. There are foundations out there now that will send you to college anywhere you want to go. Just do your job."
Watching Mays tell his story and connect with a younger group of fans was particularly striking to Baer.
"Baseball is a beautiful sport because it is the most generational sport in America by far," Baer said. "The weaving of a legend, to come back to where he played and taking that trip through time almost makes me cry, it's amazing."
Friday was all about that trip down memory lane, celebrating the Giants' historic ties with the area and the neighborhood. Even after winning the World Series in November, the Giants' brass hasn't forgotten the role the New York Giants played in forging the team's history and identity.
"I said to the crowd [at the victory parade], 'We stand on the shoulders of giants,'" Giants managing partner Bill Neukom said on Friday. "We're here today because of what happened at the Polo Grounds and what happened at Candlestick."
This weekend's trip to New York, which also includes two opportunities for fans to see the World Series trophy and a private reception Saturday night, represented a kind of homecoming. Although Mays himself didn't necessarily view it that way.
"I don't think I ever left," Mays said. "I didn't go to San Francisco by choice, I was asked to go by the team. New York has always been part of my home."