HAVANA—From the windows and decks of the first American passenger ship to make this approach in nearly 40 years, the earliest glimpse of Cuba came a little after sunrise Monday morning: a long sliver of land, then a hint of distant mountains, and then buildings, the shimmering silhouette of Havana.

The most sweeping view was from the ninth level, reachable from below by an outdoor staircase, and up the final few steps came Ana Margarita Garcia, born in Cuba, taken out with her family at age six, never returned.

“Forty-eight years and eight days,” Garcia, who is the city manager for North Miami Beach, kept telling all the reporters the previous afternoon, patiently repeating herself in Spanish, " 48 años y ocho dias ." That was how long it had been since she had seen Cuba, and yes, it was true that there were many ways she might have returned before; the Obama administration has been steadily opening categories of approved travel to Cuba, and regular plane flights now leave from Miami International Airport. (An American Airlines departures board sign in Miami International Airport recently displayed Cienfuegos, Cuba, between Chicago and Cincinnati.)

But this was the way Garcia chose—on Sunday, out of the Port of Miami, the biggest passenger ship port in the world, aboard a cruise liner called the Adonia, to the sound of a long blast of horn. It was a celebratory departure, with champagne toasts, an exuberant Cuban band, and loudspeaker announcements that frequently included the word “historic.” Police boats bobbed alongside. A lone protest motorboat, " DEMOCRACIA " painted in red across its hull, chugged doggedly back and forth, undeterred by the spray of the Adonia ’s fireboat escorts.

That evening: More speeches, thumping music, more toasts. Arnold Donald toasted; he’s CEO of the cruising company Carnival, which owns the new single-ship line, Fathom Travel, which this spring obtained permits from both the U.S. and Cuban governments to bring a cruise ship full of Americans down from Miami. Giant cruise ships are a familiar sight in the harbor outside Havana, but they’re from other countries. American citizens are still bound by U.S. State Department rules that allow visits to Cuba only for certain reasons, none of them conventional tourism.

In order to obtain State Department authority for this inaugural trip—which will also make stops at Cienfuegos and the eastern city of Santiago de Cuba—the Fathom officials had to certify that everyone on board was either a journalist or participating in what U.S. officials call “people-to-people” travel, a concept meant to encourage cultural exchange but not the giant surge of American dollars that full tourism would bring.

This was complicated. There were more complications when it appeared, just weeks before the planned departure, that Cuba intended to abide by a national policy preventing any Cuban-born person from leaving or entering the island by sea. A Cuban-born Miami Herald columnist wrote an excoriating column saying a Carnival official told her that for this reason, to the company’s regret, she could not buy a ticket for the trip. Lawsuits were threatened, hasty two-country negotiations proceeded, the Cubans declared that their policy would not be applied to the Adonia—and Ana Garcia, whose life partner works for Carnival, secured a cabin on the ship.