Cuban state-run media say Gonzalez is in Ecuador this week as part of a 200-strong delegation to the 23rd World Festival of Youth and Students, which runs through Friday.
In a recent interview published on the official website Cubadebate, Gonzalez said living in Cuba afforded him more privacy than if he had stayed in the United States.
"I'm a little shy, so when I stand up somewhere and know that the whole world is looking at me and I'm perhaps the center of attention ... it's pretty tough," Gonzalez said.
"I'd rather pass unnoticed," he added.
Gonzalez was just shy of his sixth birthday when the small boat that was carrying him, his mother and a dozen others went down near Florida. Gonzalez's mother was among those who died, but he was found floating in an inner tube, rescued and taken to the United States.
A bitter court battle ensued between Gonzalez's father, who demanded the boy be returned to him in Cuba, and Miami relatives, who insisted he stay with them.
Gonzalez became a political cause celebre both in Cuba, where the government organized mass marches proclaiming his right to be with his father, and among Florida exiles, who argued it would be inhumane to send him back to Communist-run Cuba and said his mother's wish to take him to the U.S. should be respected.
The case culminated with a dramatic raid on a house where U.S. federal agents retrieved Gonzalez at gunpoint, and he was flown back to the island in June 2000.
Gonzalez has been almost entirely out of sight since then, his privacy fiercely guarded by his father and Cuban officials. He attended a military academy as a cadet for a time and is now studying industrial engineering at Camilo Cienfuegos University of Matanzas.
In the interview, which was published to coincide with his 20th birthday on Friday, Gonzalez said the young man he is today was shaped by lessons from his parents. He also spoke of his admiration for retired leader Fidel Castro, who kept close tabs on his welfare over the years.
"He always came for my birthday. I always looked forward to that moment," Gonzalez said. "I'm a person of few words (and) I clammed up when he was there, but it was enough to see him and give him that hug."
"I always remember what he told me: That I was already somebody, that the whole world knew who I was, and now what I had to do was be good at something, that's what he asked of me," Gonzalez added. "He never cared which path I took ... the intention was that I be good at whatever I did."
Peter Orsi on Twitter: www.twitter.com/Peter_Orsi