The Netherlands, who finished fourth at the two previous editions of the World Cup-like tournament, scored runs through Didi Gregorius, Josh Palacios and two from Chadwick Tromp.
"It's very, very important to win the first game -- it takes a monkey off your back, it relaxes everybody," said Netherlands manager Hensley Meulens.
"We know we have the talent. Until you win that first game though, it's like a nervous wreck."
Palacios broke open a tied game when he grounded an RBI single up the middle before Tromp followed it up with a hit that fell between two Cuban outfielders to increase the Netherlands' lead.
The win gives the Dutch, whose roster features several players with MLB experience such as Gregorius and San Diego's Xander Bogaerts, the early edge in a Pool A that also includes Taiwan, Italy and Panama.
"It's 12:00 am over there in Aruba but my whole family is up watching the game," said Tromp.
"They've always been there for me, and they're there for me again this year."
Cuba, who finished runners-up in the inaugural World Baseball Classic in 2006, scored both their runs through Yadil Mujica.
Cuba are allowing MLB players to represent them for the first time ever, but they endured a frustrating day.
Chicago White Sox slugger Luis Robert Jr. had one hit in four at-bats, while his Chicago teammate Yoan Moncada was hitless in three visits to the plate.
World Baseball Classic returns
Twenty teams are participating in the fifth edition of the World Baseball Classic.
There are four first-round groups hosted at venues in Taiwan, Tokyo, Arizona and Florida before the bulk of the knockout rounds get underway in the United States.
The tournament was last staged in 2017, with the United States finally winning the title for the first time with a victory over Puerto Rico at Dodger Stadium in Los Angeles.
The pandemic forced the postponement of the tournament in 2021, meaning the United States are only now launching their title defence with a team bristling with stars from Major League Baseball.
The USA play Britain in their opening game on Saturday at Chase Field in Phoenix, the home of the Arizona Diamondbacks.