"Hustling is important," the rookie right fielder said. "Every time, you need to hustle to get better. My dad, he would tell me all the time: 'Hey, keep going, keep going. Do everything right. If you do everything right, you will be famous.' You never know."
Ranked by MLB.com as the Marlins' No. 6 prospect, the organization knew it would only be a matter of time before Ozuna advanced to the big leagues. But no one foresaw how quickly the rise would come and the circumstances surrounding it.
Ozuna was playing at Double-A Jacksonville, and he was starting to heat it up at the plate. His performance was elevating at the same time the Marlins absorbed a big blow.
On April 29, in the 10th inning of Miami's 5-4 win over the Mets in 15 innings, Stanton strained his right hamstring. The next day, Stanton was headed to the disabled list, and Ozuna was making his MLB debut in Miami.
Thus far, the big league stage is bringing out the best in Ozuna, who started off his career with a six-game hitting streak, which is two games shy of Alejandro De Aza's franchise record for a player to begin his stint with the Marlins in 2007. In those six games, Ozuna had 11 hits.
In an organization with highly touted prospects like Jose Fernandez and Christian Yelich, Ozuna has played under the radar.
"He's always been on my radar screen because he's an RBI guy," Marlins vice president of player development Marty Scott said. "He will get his share of strikeouts, and he will have his streaks of highs and lows. As long as he remains consistent and does the things he's doing, he will be fine."
Yelich, still at Double-A, is a gifted 21-year-old with a pure swing. Ozuna is more of a power threat.
"Yelich is a no-brainer [prospect]," Scott said. "He has one of the finest swings I've seen from the left side for a young kid. He has great makeup and great work ethic. I think Yelich is going to be a perennial .300 hitter.
"Ozuna, with his throwing arm, and his ability and his accuracy, he's going to excite the crowd. He will make some unbelievable throws from time to time to nail runners and electrify the crowd."
Ozuna has already showcased his arm, recording three outfield assists during Miami's 10-game road trip, which concluded on Sunday. In back-to-back games at Dodger Stadium, Ozuna picked up assists. He had an impressive throw on Sunday to get speedy Carl Crawford attempting to tag up at second on a fly out to right field.
"I think Carl was a little surprised," Marlins manager Mike Redmond said. "We're talking a Vladimir Guerrero-type arm."
Ozuna may not hit for average like Yelich, but Scott wouldn't be surprised to see seasons of .280 with 30 homers and 100 RBIs. Through 12 big league games and 46 at-bats, Ozuna is hitting .326 with five doubles, a home run and five RBIs.
All smiles and a happy-go-lucky personality, Ozuna has added excitement to a youthful team that is undergoing growing pains. He can also play all three outfield spots, offering the organization flexibility for when Stanton returns.
"What he's done is energize this team," Redmond said. "He's showing that youthful exuberance where he's just going out there playing, having fun and has got nothing to lose. That's the attitude we should have all the time."
For all the energy Ozuna is providing now, it took a moment of laziness a year ago for him to get a wakeup call. Last season at Class A Jupiter, Ozuna was called into the office when he didn't run hard to first base on a routine out. Ozuna sat down with Hammerheads manager Andy Haines and Scott.
"We talked about attitude and hustling all the time, giving something back to the fans, and always being humble," Scott said. "We basically just talked about respecting the game -- playing the game the way it's supposed to be played.
"We told him, 'We know if you hit the ball back to the pitcher, you're going to be disappointed. If you pop out to the infield, you're going to be disappointed. If you strike out, you're going to be disappointed. We already know that, so get over it.'"
Scott offered some perspective and gave Ozuna a challenge. Sometimes there is a need to play a "game within a game" to offer incentive.
So Scott challenged Ozuna on every time he hit a routine fly ball. The test was to see how close he could get to second base on a ball in the air.
You now see Ozuna trying to get within 10 feet by the time the ball is caught. That's the kind of effort the Marlins are looking for to boost the club. Occasionally, there is a payoff.
Ozuna opened the Minor League season on the disabled list due to a broken bone in his left wrist. When he was playing in a rehab game on a back field in Jupiter, Fla., he hit a fly ball. It was relatively routine.
Not taking anything for granted, Ozuna was in full sprint, and the unexpected happened -- the ball dropped. By that time, Ozuna was standing on second.
And after the lecture last year, Ozuna singled to center for the Hammerheads, and he picked up on the opposing defense going through the motions. The center fielder made a soft, arching throw back to the infield. With the ball floating in, Ozuna dashed to second, and the ball got by the middle infielders.
Ozuna didn't stop there. The third baseman retrieved the ball, and the pitcher was standing on the mound, so Ozuna dashed to third. On hustle, he took three bases on a single to center.
The extra effort is driving Ozuna to stick around for a while. If he keeps performing, whenever Stanton returns (and he is not yet close), the Marlins will find a place in the lineup for him -- either left field or center. That situation will take care of itself down the road.
For now, Ozuna is adapting to being an everyday player.
"I'm living my dream now," he said. "I never thought I would be over here playing in these big cities."