Havana (CNN) President Barack Obama touched down in Cuba on Sunday , definitively ending a half-century of estrangement in a dramatic personal demonstration of his core foreign policy principle of engaging America's enemies.

It's a shift that the change-minded president hopes will nudge the Communist government here to grant more freedoms to its people and open new economic channels for American businesses. The President and his allies also hope a successful détente will offer something bigger: a lasting example of diplomacy's power in dealing with longtime foes.

Just before Obama stepped from Air Force One -- carrying an umbrella as a persistent rain fell on the tarmac -- he sent a message to Cubans on a platform that until recently would have been unheard of in the repressive regime.

"¿Que bolá Cuba?" he wrote on Twitter, using an informal Cuban greeting. "Just touched down here, looking forward to meeting and hearing directly from the Cuban people."

¿Que bolá Cuba? Just touched down here, looking forward to meeting and hearing directly from the Cuban people.

On Sunday, his interactions with everyday Cubans were carefully calibrated. He toured the Cathedral of the Virgin Mary of the Immaculate Conception, greeting Cardinal Jaime Ortega, a key proponent of improving ties between the U.S. and Cuba. Crowds had gathered in the faded colonial streets of Old Havana to glimpse Obama and his family as they passed through on foot.

Later in the evening, Obama dined at a "paladar" -- one of hundreds of privately-run restaurants that only recently became permissible in the state-run economy.

Those types of businesses -- along with new investments from American firms -- give U.S. officials hope that Cuba is on a path to finally opening its economy after decades of isolation.

But the final verdict on Obama's Cuba policy has yet to be rendered. Those economic changes have been slow, and human rights are still blatantly ignored in parts of the island.

That was illustrated Sunday, when scores of anti-Castro dissidents from the group Ladies in White were arrested and detained after their weekly protest in Havana. CNN witnessed dozens of protesters being driven from the site in buses.

Jose Daniel Ferrer, a Cuban dissident who was imprisoned for eight years beginning in 2008, said Obama could act like President Ronald Reagan, demanding immediate improvements in human rights just as Reagan demanded the Soviet Union "tear down this wall."

But Ferrer, speaking in an interview with CNN in his home Sunday, conceded that even incremental change is beneficial to the island's politically oppressed citizenry.

"Obama's visit is good for the people and good for the cause," he said. Ferrer is among the dissidents meeting Obama on Tuesday.

Challenges aside, the sight of Air Force One landing at Havana's Jose Marti Airport in the early evening on Sunday nonetheless represented a diplomatic metamorphosis that few could have imagined even five years ago.

"My view is that this is the beginning, not the end, of what is going to be a journey that takes some time," Obama told CNN in an interview ahead of the trip.

"This is a matter of us engaging directly with the Cuban people and being able to have candid, tough conversations directly with the Cuban government," Obama said. "We will have more influence and have greater capacity to advocate on behalf of the values that we care about when we're actually talking to them."

The presidential trip to Havana is the culmination of a three-year effort to restore ties to the island, which sits 90 miles from Key West, Florida, but has long been off-limits for most American visitors. For decades, the island was regarded as a Cold War adversary, a forbidden place run by bearded strongmen that residents fled on makeshift rafts.

Following in the path of the Obamas

With his family in tow, Obama hopes to change that perception, highlighting the country's emerging private economy and meeting with outspoken opponents of the Castro regime. Before he departed, Obama met with Cuban-Americans in a bid to garner support for his diplomatic thaw, which is still met with skepticism among many in the large Cuban diaspora in South Florida and elsewhere. Several of the participants in the meeting will join Obama on his trip.

With relaxed restrictions on who can travel to Cuba, many more Americans will now able to follow the Obamas' lead . And administration officials hope improved economic ties can foster a new dynamic between individual Cubans and Americans.

But critics of Obama's policy, including outspoken Cuban-American members of Congress such as Republican Sens. Marco Rubio and Ted Cruz and Democrat Robert Menendez, argue the opening only rewards an authoritarian regime -- one that has yet to show much sign of reform.

Obama will tend to the Cuban government while here, sitting Monday for his third bilateral meeting with leader Raul Castro since taking office and participating in the usual trappings of an official presidential visit, including a formal welcoming ceremony and a state dinner at the Revolutionary Palace.

But he'll also peel away for less formal encounters, allowing the presidential spotlight to also shine on ordinary Cubans living in a new era, including during an address to the Cuban people during a speech broadcast on state television, and the meeting with anti-Castro dissidents.

Before he departs Tuesday, Obama will watch the Cuban national baseball team play the Tampa Bay Rays, in town for an exhibition game as U.S. Major League Baseball works to update immigration rules for Cuban players

The sight of a sitting American president setting foot on the island will be a novelty for most Cubans. The last U.S. leader to visit was Calvin Coolidge, who voyaged into Havana Harbor on a battleship in 1928. This time, Obama's aides want to project a far different image.

"There's great anticipation here for the visit," said Jeffrey DeLaurentis, the top American diplomat in the recently reopened U.S. Embassy in Havana. "We want to broaden the engagement underway."

That engagement began in December 2014, when Obama announced he was working to reopen long-frozen diplomatic ties to the island. The declaration was punctuated by the release of Alan Gross, an American prisoner in Cuba, in exchange for Cubans held in American jails.

Since then, the U.S. government has steadily removed restrictions on travel and commerce between the neighboring countries. Last week, officials announced some of the biggest changes, including allowing Cubans to open U.S. bank accounts and permitting Americans to travel here individually, rather than as a group, for educational or cultural reasons.

You've got mail

The first mail flight between the two countries since 1968 arrived in Havana from Miami on Wednesday, carrying on it a letter from Obama to a Havana coffee shop owner, a response to a series of missives he'd received ahead of his trip.

It's still difficult to get here as an American; charter flights remain the only option until U.S. carriers resume regular flights later this year.

But once those flights are underway, U.S. officials expect a steady flow of American visitors that will outlast Obama's presidency.

"We very much want to make the process of normalization irreversible," said Ben Rhodes, Obama's deputy national security adviser and a chief draftsman of the Cuba policy.

Rhodes and Obama have cited Cuba -- along with a brokered deal with Iran to end its nuclear program -- as successful evidence of the President's 2009 inaugural vow to "extend a hand" to traditional U.S. foes.

But without congressional action to lift a longstanding trade embargo, there's little Obama can do to fully restore economic ties to Cuba. He told CNN he didn't expect lawmakers to take action while he's in office.

"My strong prediction is that sometime in the next president's administration, whether they are a Democrat or a Republican, that the embargo in fact will be removed," he said.

The current Congress has shown little appetite for such a move.

"There has not been a single democratic opening; not a single change on the island in human rights," Rubio, at the time a GOP presidential candidate, said during a CNN debate last week . "In fact, things are worse than they were before this opening."

He continued, "The only thing that's changed as a result of this opening is that now the Cuban government has more sources of money from which to build out their repressive apparatus and maintain themselves there permanently."

While most Republicans in Congress have expressed little interest in lifting the blanket restrictions, Obama has found some bipartisan support.

"If there's one policy that has aided the Castros, that's kept them in power, it's the travel ban and the embargo," Sen. Jeff Flake, an Arizona Republican who will travel with Obama to Cuba, told CNN in an interview. "It's given them a convenient excuse for the failure of socialism. So we ought to remove that crutch. We're doing so. And I think we'll move ahead more quickly now."