HAVANA — Brushing past profound differences, President Barack Obama and Cuban President Raul Castro will sit down Monday at Havana’s Palace of the Revolution for a historic meeting, offering critical clues about whether Obama’s sharp U-turn in policy will be fully reciprocated.

For Obama, there’s no better place than Havana to show that engagement can do more than isolation to bring about tangible change in the tiny communist nation. Yet for the Cubans, the glaring question is whether their own government is ready to prove the ambitious diplomatic opening is more than just talk.

Obama opened the first presidential visit to Cuba in nearly 90 years on Sunday when Air Force One touched down in Havana. Strolling through the grand cobblestoned plazas of Old Havana with his wife, Michelle, and daughters Sasha and Malia, Obama created an indelible image for both Cubans and Americans of the peacemaking that he and Castro have cautiously but doggedly pursued.

“That’s the future that we hope for: young American children, young Cuban children, by the time they’re adults, our hope is that they think it’s natural that a U.S. president should be visiting Cuba,” Obama told American diplomats assigned to the newly reopened U.S. Embassy. “They think it’s natural that the two peoples are working together.”

Indeed, the U.S. and Cuba are working more closely together now than at any time since relations took a nose dive amid Cuba’s 1959 revolution. Yet while Americans are now flocking to Cuba in greater numbers, closer ties have yet to bring about the degree of change that many Cubans hoped would follow after Obama and Castro moved to normalize relations 15 months ago.