At the time of his second such moment - meeting Robert F. Kennedy at a Chicago airport two years later - Vidal was on his way to an orphanage in Pueblo, Colo. He was one of thousands of Cuban children flown to the U.S. in Operation Pedro Pan following Castro's revolution.
"I would measure that as the most traumatic experience of my life," said Vidal, Denver's first foreign-born mayor, of being separated from his family. "To leave my parents and come to this country and not know what we were facing, not knowing the language, not knowing the culture."
Vidal, 59, honored his parents, Roberto and Marta Vidal, at his Jan. 12 inauguration as he replaced his boss, Democrat John Hickenlooper, who is now Colorado's governor.
"I stand in front of you today as a Cuban immigrant whose life - if only for a brief moment - has become directly intertwined with our city's destiny," Vidal declared. "Like other immigrants, both legal and illegal, I came to this country in search of a better life."
Denverites have embraced the interim mayor, whose term officially ends July 18. He affirmed this week he is not seeking election, although he touched off a political flap by briefly flirting with the possibility.
"I think he's viewed as a wise elder. He's one of those people who, when he talks, people listen," said Bob Murphy, mayor of suburban Lakewood, who's known Vidal since Vidal headed a regional council of governments.
"I think it's almost poetic justice," said Denver City Councilman Paul Lopez. "His story is proof that if you work hard and never give up and work in the service of others, it'll pay off."
Vidal was born in Camaguey, Cuba. His upper-middle class family had a cook, a gardener and a several nannies. The day he met Castro, Vidal's parents lifted him and his two brothers toward a tank Castro was riding in as confetti rained down.
When Castro's government began seizing private property, Vidal's parents told him they were taking a vacation. It culminated in what Vidal called "probably the most terrible day of my life."
Vidal was 10 when he and his 11-year-old twin brothers were placed in Colorado's Sacred Heart Orphanage in 1961.
They were reunited with their parents three years later - the point Vidal considers the real beginning of his family's immigration story.
Everyone had to chip in with work. For a time, the family managed an apartment complex and Vidal and his brothers cleaned, mowed lawns and handled maintenance complaints from residents. They bought their clothes from thrift stores, and meals were sometimes scarce.
Vidal chronicled his family's struggles in a 2007 book, "Boxing for Cuba: An Immigrant's Story of Despair, Endurance, & Redemption." He said he wrote the book for his three children from a first marriage.
In 1973, Vidal graduated from the University of Colorado at Denver with a civil engineering degree. He worked at the Colorado Department of Transportation for 23 years, including five years as its executive director. That job ended in 1999 when Republican Gov. Bill Owens took office and appointed someone else.
Wary of accepting another political appointment, Vidal turned down Hickenlooper's request three times that he become deputy mayor and public works manager.
Vidal then saw a "skinny, dorky, geeky guy" in a cameo appearance in "The Man from Elysian Fields," a film directed by Hickenlooper's cousin, George Hickenlooper. The geeky guy was Hickenlooper. Vidal and his wife, Gabriela Cornejos, looked at each other and said, "It must be a sign from God!" He accepted the mayor's offer in 2004.
Vidal urges greater acceptance of immigrants and opposes initiatives that would separate families or deny education or health care for illegal immigrants. He calls the federal Secure Communities program, which aims to identify illegal immigrants through fingerprinting when they're arrested, "worrisome," and says it should be strongly monitored when it's implemented in Colorado.
"I feel like I owe it to other immigrants to advocate for them," said Vidal, who highlights the fact that his wife is a Chilean immigrant - and a 30-year civil servant in Colorado.
Vidal says he wants to take a long-awaited break to see two grandsons in South Korea, and perhaps return to Cuba.
He visited the island nation for the first time since childhood in 2001 and, he said, "spent most of my time crying, seeing how difficult life would've been had I stayed."