The Atlanta Braves rookie was on a small boat for several days with about 35 others. There was no food or fresh water. Some got seasick. All were scared.
But Escobar was determined to get to the United States.
"Everything was here," the 24-year-old said through a translator, looking back three years. "Nothing was there."
Escobar made it to Florida in the fall of 2004, realizing the first part of his dream. In early June of this year, the other half of his dream came true when Escobar made his Major League debut.
"Every baseball player has to struggle to make it," Escobar said. "For Cubans, it is a little harder. You have to want to play even more."
Asked about his escape on the small boat, Escobar said, "We were between life and death." That's why Escobar makes his joy so obvious.
"You can see how much he loves to play," Braves manager Bobby Cox said.
And Escobar has shown he can play very well, hitting over .300 as a rookie and flourishing while given the opportunity to fill in at shortstop when Edgar Renteria was sidelined for about a month.
But adjusting to life and baseball in the United States hasn't always been smooth.
It wasn't easy being away from family or having to adjust to the way the Braves wanted him to play the game he so loved.
Escobar was told he could no longer constantly whistle -- something he'd always done on the diamond. No more showboating. No more aggravating opponents, and sometimes even his own teammates.
"No, no, no," said Escobar, who clashed with manager Jeff Blauser last season at Double-A Mississippi.
But it was a more mature and comfortable Escobar in Spring Training this year, and at Triple-A Richmond to start the season. His exuberance has been a positive, not a negative, with the Braves.
"I'd heard some things," Cox said. "But he's fit in great here."
Off the field, Escobar is also fitting into life in America. He was married this year to a woman he met in Miami. His father and sister joined him first in the United States. When his mother finally got out of Cuba this summer, the family was complete again.
"It is hard being away from the people you love," said Braves backup catcher Brayan Pena, a fellow Cuban defector. "That's why making it to the Major Leagues means so much. It is everyone's dream, and you have to sacrifice a lot to try to make it come true."
Pena and Escobar grew up together in Havana, playing on the same teams, and at first even sharing the same glove.
They also had the same goal.
Pena made his escape first, fleeing the Cuban junior team at a tournament in Venezuela. He was 17, a year older than Escobar. He didn't even dare tell his roommate what he was going to do.
"I couldn't think about getting caught," said Pena, who told a guard he was going to the restroom. "I couldn't. If you do, your fears take over."
Pena made it, eventually reaching Costa Rica. About a year later, the Braves signed the switch-hitter to a bonus contract and he began moving up through the Minor League system.
Meanwhile, Escobar remained in Cuba, baffled that Pena hadn't tried to take him along. "But I couldn't," Pena said.
"I was surprised, but I knew in the bottom of my heart that one day we would be together again," Escobar said.
With his friend gone, security tightened around Escobar. But the shortstop's desire to make it to the United States himself some day never waned.
Five years after Pena's departure, Escobar finally got his chance.
Five other players were on the boat with Escobar when he left Havana. He is the only one who has made the Majors so far.
"When you are desperate, you will do anything," Pena said.
After checking on Escobar with Pena, the Braves drafted the slick-fielding right-handed hitter in the second round of the 2005 First-Year Player Draft. In two years, the former boyhood friends were teammates in the Major Leagues.
"We always dreamed about playing for the Braves," Pena said. "They were always winning and we liked the uniforms. We saw a picture and they looked so white."
Now Pena and Escobar are wearing those uniforms.
"The dream came true," Escobar said. "I don't just play for myself. I also play for Cuba."
Escobar's biggest thrill may have come when he homered off countryman Orlando Hernandez of the Mets in New York.
El Duque was one of Escobar's idols growing up. Best yet, the game in which he homered was televised to Cuba.
"Everyone could see it," Escobar said.
And see how far he'd come.
Guy Curtright is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.