"I was like 'Wow, what is going on here?' " he said. "What is this game?"
Jarrin eventually made it into baseball, and through his work, has helped shape the landscape of Spanish broadcasting. A Hall of Fame broadcaster, the living legend remains in love with that intriguing sport he first saw a half-century ago.
"I hope people can see someone in me who came to this country without knowing the language, without baseball experience and without knowing anybody, but through hard work and responsibility, was able to go places," Jarrin said. "I hope that I can be an example to many people, because it is an American dream. I love Ecuador, my home country, but this is a great country that has given me the opportunity to do what I have done."
He wasted little time following his dream.
Not long after the 1955 World Series, Jarrin started inquiring about baseball. He began watching the Hollywood Stars of the Pacific Coast League and the Dodgers, after they relocated to the West Coast in 1958.
He was working with KWKW when the radio station acquired the rights to broadcast Dodgers games in Spanish. Jarrin was asked to be one of the two broadcasters, teaming with Rene Cardenas.
No way. Not yet, anyway.
Jarrin refused in 1958 because he didn't feel he was prepared for the task. He spent the year going to every game he could and reading every book about baseball. In 1959, Jarrin made his debut with Dodgers and assumed he would only work in baseball for six or seven years before returning to news reporting or being a boxing or soccer commentator. But 46 years later, he is still calling games.
"I was at the right place at the right time," he said. "I have been extremely lucky in this country. I have never lost one minute of sleep worrying about tomorrow because I have always been able to have three and four jobs at the same time."
Jarrin credits the Dodgers, behind the effort of Walter O'Malley, as being the first organization to look into incorporating the Spanish language into broadcasts and making the Hispanic market a priority. Not surprisingly, the Dodgers were the first team to have bilingual coverage of games on a regular basis. Although the Spanish broadcasters did not travel with the team for the first few seasons and covered only home games and weekends, they eventually started traveling to San Diego and San Francisco in the late 1960s.
In 1973, Jarrin started traveling with the team full time as the club's No. 1 Spanish broadcaster. He jokingly likes to say, "They don't play if I'm not there."
What is no laughing matter, though, is the fact Jarrin has seen the game change through the years -- for the better.
"When I started in 1959 and in the early '60s, you could count on one hand the really good Hispanic players," Jarrin said. "I'm talking about Felipe Alou, Juan Marichal, Roberto Clemente and Orlando Cepeda, and that was it, at least in the National League. I know there were not that many in the American League, but there were some."
What makes Jarrin particularly proud is that many of today's All-Stars are Latino. Moreover, some of the game's most popular players -- like Alex Rodriguez, Manny Ramirez and Ivan Rodriguez -- are among the highest paid.
"It's great to see the players on the field, and it's fantastic to see the Hispanics coming to the ballpark to watch games," he said. "When I joined the Dodgers, there were probably 8 to 10 percent at the most -- Hispanics coming to the games. Now, Dodger Stadium has between 38 and 40 percent [Hispanic] fans coming to the game each night, and that talks very loudly about the power of the Hispanic market."
What also makes Jarrin smile is the growing number of big-league games being broadcast in Spanish. He shies away from being called a pioneer and a role model because "that's what parents are for." Instead, he chooses to talk about what is going on in Spanish broadcasting across the country.
"I think I have done something to open the doors to some of my Hispanic colleagues working in baseball," he said. "When I was inducted into the Baseball Hall of Fame in 1998, I knew that -- along with the accolades I got -- I knew it was a responsibility to open the doors for my colleagues in the field."
Pepe Yniguez and Fernando Valenzuela join Jarrin in the Spanish radio booth.
"For me, the experience with Jaime is a beautiful one," said Yniguez, who is in his seventh season with the Dodgers. "More than just a professional, he is gentleman. He deserves all the praise because he has done it with talent and also hard work. To work with him is a great thing, and it better be. I spend more time with him than I do my wife, so he better be fun."
Among Jarrin's honors include enshrinement in the California Broadcasters Association Hall of Fame and the Hispanic Heritage Baseball Museum as well as receiving the Southern California Broadcaster Association President's Award.
In 1998, he became the second Spanish broadcaster inducted to the National Baseball Hall of Fame, joining Buck Canal as the recipient of the Ford C. Frick Award, given annually to a broadcaster "for major contributions to the game."
"The Hall of Fame is the biggest honor you can get, and it's something you can't cherish enough," Jarrin said. "It's for your family and your sons and the sons of your sons. July 26, 1998, was a grand day, and I don't have the words to describe what it means to be among the best ever in baseball."
Jarrin is living a dream and will continue to work as long as his vocal cords allow. The reasons for his success and the rise of Spanish broadcasting are simple.
"In our culture, we work very hard," he said. "We love soccer, we love boxing and we love baseball. If you offer them something in their own language, the Hispanic fans will listen, and then they will come to the games."