He didn't leap any tall buildings in a single bound. Not that we know of, anyway.
Abreu's on-field performance in April did earn him two awards: player of the month and rookie of the month. While these awards are basically meaningless, only Abreu and Cuban countryman Yasiel Puig have won both in their first month in the bigs. At least Puig, who did it last June, got to warm up in the minors.
While he doesn't have the worldwide appeal of Puig, Abreu is making quite a name for himself in Chicago.
In a town starving for a meaningful baseball story, Abreu is the best thing to happen here since, well, Sox pitcher Chris Sale. Beside those two, it's slim pickings in Chicago, where hope is losing to apathy.
Chicago baseball started its annual convention Monday at Wrigley Field with the first of four "crosstown" games and Abreu was the top story for two sub-.500 teams.
The first question I had for White Sox general manager Rick Hahn on Monday afternoon was, "Do they give you the GM of the Year award now?"
"Oh, God," Hahn said. "Absolutely not."
Hahn lacks the gravitas and dramatic pauses of his boss Kenny Williams, but even he knows he did real, real good by signing Abreu to a historic $68 million deal this past offseason. No Cuban player had ever received that much money as a free agent. So far, the 27-year-old Abreu has been worth every penny.
Abreu showed no jitters in moving from Cuban baseball to the Sox, a team with a rich history of Cuban players, and he said he has kept his baseball routine relatively intact as he moved from ancient stadiums to taxpayer-funded palaces.
"I had a little anxiety of getting to know baseball here in the United States, but I wouldn't call it nervousness," Abreu said through a translator. "It was just anxiety to go through it and be able to experience it. Now, one month into it, it's a great thing. I'm excited."
He also has learned the wonders of our gluttonous culture.
Playing in a city with world-class steakhouses, Abreu, listed at 255 pounds, is enamored with Brazzaz, one of those Brazilian joints where they bring you carved meat until you're wheeled to your car or an ambulance. Welcome to America, right?
"I have been to several places and have seen where they have a lot of food, but I have never seen anything like that," Abreu said. "And it's so good."
That's kind of how White Sox fans, not to mention baseball writers, feel about Abreu.
Like any good executive, Hahn tried to downplay expectations for Abreu, but the time for modesty is over.
"You know what, it's a great testament to him," Hahn said. "I think I've spent more time when we talk about Abreu, talking about the fact that this is a process and his signing needs to be evaluated over the course of six years and not a month. And I really should just take all that back and, after one month, let's just say it was a great deal."
Hahn then got serious and went on to warn of inevitable setbacks and slumps. Pitchers will adjust as the scouting services get Abreu in the crosshairs.
So I asked Sale, the Sox's injured ace and the reigning "Best Player in Chicago," just how pitchers will adjust to Abreu.
"I don't know," he said. "I'm just glad he's on our team and I don't have to make adjustments for him. Talk about his last home run he hit, it was 95, 96 mph -- in, in -- and he got the barrel to it. It's unbelievable."
That home run, given up by Indians pitcher Corey Kluber in the first inning Sunday, was listed as a 93-mph sinker, but Sale's assessment was correct. Abreu yanked the inside pitch to deep left, a quick and violent line drive for his 12th home run.
Abreu's game-ending grand slam April 25 against the Rays at home is probably his most memorable home run, but that's not Hahn's favorite Abreu game.
"The day that stands out for me was the day in Colorado where he turned on the ball and showed that power on the inner half," Hahn said of the 15-3 Chicago victory April 8, in which Abreu went deep twice. "He hit the ball out to left and also hit one to the opposite field. You saw that tower-to-tower power we had talked about on display in a single game."
Abreu's teammates, meanwhile, have trouble coming up with a single favorite Abreu moment, aside from the grand slam.
"I feel like he's hit a whole lot of them in a short amount of time, so it'll take me a minute to sit here and think about them," fellow slugger Adam Dunn said.
Abreu has assimilated well, thanks in part to a support system that includes three Cuban teammates. Despite the language barrier with the American players, Sale said Abreu is funny and energetic in the clubhouse. Asked if they have any nicknames for the slugger, the pitcher laughed.
"Uh, 'Amazing,'" Sale said. "'Unbelievable,' 'What a hitter!' 'Uh-oh!'"
"What a hitter" knocked in the Sox's first run with an opposite-field sacrifice fly in their eventual 3-1, 12-inning victory on Monday. Abreu's success has been contagious for a hot-hitting Sox team, Sale surmised, and he doesn't see the Abreu Flu getting cured anytime soon.
"I don't think it's a fluke, what he's done," Sale said. "Some people might be like, 'It's beginner's luck,' this, that and the other. Unfortunately for the rest of the league, that's not the case."