HAVANA, Cuba – The best part was when the grown-up ballplayers picked up the small Cuban boys and girls, weary from a long ceremony that would mean nothing to them, and carried them from the field on their hips or across their arms like gladioli bouquets.

Dressed in tiny red and blue baseball uniforms, the children idly twirled their little Cuban flags, watching them flutter in a breeze that had drawn the gray clouds and run off the morning sun. They’d long tired of the talk and formalities.

The time for baseball at Estadio Latinoamericano would come soon enough, but for two days the other grown-ups had tended to this next generation of Cuban boys and girls. The baseball players among them. The doctors and machinists and shopkeepers and fishermen among them.

They’d get to the baseball, this exhibition game between the Tampa Bay Rays and the Cuban national team, but first the grown-ups held the hands of the children, asked them their names, told them theirs, then hoisted them into the air and carried them the rest of the way. Tuesday had been another one of those terrible days in the world, yet another day to soothe the children.

Hours later, President Barack Obama arrived at a baseball field here, sat beside the Cuban president, man-hugged Derek Jeter, watched a cote of doves spray from the center-field batter’s eye, flung out his arms to signal safe on the Rays’ first run, then departed with a wave, all in a little more than an hour.

It was supposed to be meaningful, and it was, as many hoped it would be. Obama arrived later than scheduled, so a good portion of pregame ceremony involved everyone in the stadium standing on their seats and staring at the tunnel from which Obama and Cuban President Raul Castro would emerge. Daughters Malia and Sasha led their parents to the front row, the president in a white dress shirt and sunglasses, the coolest dude in the joint with the possible exception of Jeter. He waved and the people cheered. Castro waved and they cheered louder.

Cuban players trotted from their dugout to honor Castro and several minutes later Rays players introduced themselves to Obama, performing the handshake-through-the-backstop-netting that is singular to baseball. The Cuban people waited patiently. The children were herded back to their parents.

Nearly 90 years had passed since a sitting U.S. president had been among them. For this they came to the ballpark hours ahead of time, passed a batting cage practically in the parking lot where Rays hitting coach Derek Shelton worked with one of his players – “I always flip [baseballs] in front of 10,000 people,” Shelton said with a laugh – and stood in long lines. They inched through a metal detector that pinged and blazed red without pause, which appeared to concern no one. They found their seats in this old ballpark that had seen countless baseball games, that had received a fresh coat of paint for the occasion, and hadn’t seen anything quite like this before. Rumor had it these particular fans had been selected to attend by the Cuban government, though it would be difficult for an outsider here to discern where the dark conspiracies end and the practiced paranoia begins.

The game, or at the very least the spirit of this game, lived beyond such notions. While honoring the place baseball has – and has had for a very long time – in both cultures, the game tended to today. It put forty-something thousand people in the stands and two decent teams on the field and drew international interest for it. More, the game was played for tomorrow. For the next 19-year-old who must choose between home and a dark journey away.

By the end of Major League Baseball’s stay, commissioner Rob Manfred had grown more optimistic for a plan to have Cuban players come and go from the island without past perils. Broader, credentials hung from the necks of at least a few Americans in the crowd that read, “U.S. Embassy, Havana,” and the day before Obama had predicted the end of the U.S. embargo.

The big things will take time, because they are big things. But the smallest endured.

Angel Hernandez, the major league umpire who worked first base Tuesday, arrived in Cuba carrying an aluminum bat wrapped in a garbage bag. The bat was for a retired Cuban baseball player Hernandez had met in December, who plays softball now and had mentioned the poor condition of his equipment. Jeff Idelson, president of baseball’s Hall of Fame, presented Cuban center fielder Roel Santos with a Hall of Fame jersey, remuneration for Santos having donated one of his own to the Hall. After the Rays beat the Cubans 4-1, players from both teams hugged and exchanged jerseys. Chris Archer, the Rays’ best pitcher, held Frank Morejon’s No. 45.

“Wonderful, fantastic,” Archer said of his Cuban experience. “Opening ceremony, I honestly had to fight some tears. It was emotional.”

Dayron Varona once wore the Cuban jersey. On Tuesday, he started in right field and batted leadoff for the Rays. He had feared the reception on his return to Havana, but the people treated him warmly.

“I’m a Cuban,” he said. “Because I made the decision to leave here doesn’t make me less of a Cuban.”

Yeah, that’s part of what the grown-ups spent the week sorting out. For a few hours, none of those differences seemed to matter. On the stadium scoreboard in center field an American flag flew to the right of Cuba’s flag. One president sat beside the other, one of them perhaps a bit over the top in his enthusiasm for a run scored in an exhibition game. But still. Perhaps everyone went home feeling better about what is here and what can be here, given some time and given some perspective.

It helps to see it. To hold it in your arms. To remember who this is for.

“They were so young,” Rays first baseman James Loney said. “They might not even remember. But, for those who do …”

For those who do, it might very well be the best part.