Dreams are coming true for Ny Traffic trainer Saffie Joseph Jr.

Saffie Joseph Jr. was driven by “crazy ambition” when he left his native Barbados against the advice of his father and arrived in South Florida with two horses to train in 2011.

Two years ago, he wondered if he had been crazy and foolish.

He lacked the owners and therefore the horsepower to compete at the highest levels at Gulfstream Park and elsewhere. He began to believe that his dream of reaching the Kentucky Derby and winning it would never be more than a dream.

“I don’t think we’re going to break through,” he confided in his father.

By this time, though, Joseph Sr. was all in. “We’ve come too far. We’re not turning back. We only have one way to go. We have to succeed,” he told his son.

Joseph Jr. returned to the barn with renewed determination that has been richly rewarded. He captured his first Grade 1 victory last September when Math Wizard, a former $25,000 claiming horse, pulled a stunning upset in the Pennsylvania Derby at 31-1.

And now the 33-year-old conditioner is, indeed, bound for the Kentucky Derby with Ny Traffic. The New York-bred rates at least a puncher’s chance of toppling Tiz the Law on the first Saturday in September. He staged a furious rally that missed overtaking well-regarded Authentic by a nose in the July 18 Haskell Stakes (G1) at Monmouth Park in his most recent start.

“Our dream when we came here was to get into it and eventually win it,” Joseph Jr. said of the Derby. “Obviously, we have a long way to go. But to be in this position, we’re in awe.”

He also has a 3-year-old filly, Tonalist’s Shape, who ranks among the elite members of her class.

When it comes together for a young trainer, it often seems to happen all at once. Joseph Jr. won at a torrid 26 percent clip last season, with 95 winners from 370 starters for earnings of $3,877,156, according to statistics compiled by Equibase. As difficult as the pandemic-affected year has been for everyone, he entered this past weekend winning at a 23 percent rate, with 79 wins from 351 starts and earnings of $3,113,111.

John Fanelli, who co-owns Math Wizard and Ny Traffic, is not surprised by his trainer’s breakthrough. “He sleeps, eats and breathes horses,” he said, adding, “His whole family is racing. That’s all he knows.”

Joseph Jr. is a third-generation horseman. He was 22 when he became the youngest trainer in Barbados history to produce a Triple Crown champion. Areyoutalkintome accomplished the sweep in 2009.

Ny Traffic, a New York-bred son of Cross Traffic, offers an example of his ability to help a horse fulfill its potential.

“He just kept getting better and better,” Joseph Jr. said. “In January, if you had told me he would be my Derby horse, I would never have expected it.”

Ny Traffic has finished second in each of his last three starts: the March 21 Louisiana Derby (G2) at Fair Grounds, the May 23 Matt Winn Stakes (G3) at Churchill Downs and the Haskell. Although he was a relatively meager $22,000 private purchase for Fanelli, he ranks fifth on the Churchill Downs leaderboard, with 110 qualifying points.

“Obviously, he has to improve to be with the horses at the top, but he’s shown progression,” the trainer said. “He should make another jump forward. If he makes another jump forward, he’s right there.”

Ny Traffic is training impressively at Saratoga Race Course. He covered five furlongs in 59.03 seconds last Thursday, ranking second of 25 workers at the distance. He is expected to ship to Churchill Downs at the end of the month.

“I think we go there with a chance,” Joseph Jr., said. “From the numbers standpoint, he fits. When they fit on all the handicapping tools, that’s very important to me.”

A Derby victory — even a strong performance — would surely be a boon to an operation that has grown to about 100 horses. The quality seems to improve almost daily. It took time, but Joseph Jr. has assembled a staff that Fanelli describes as “amazing.”

“I think he’s going to be in the top five every year for as long as he wants to be,” Fanelli said. “Once he gets the stock, there are not too many people who can do what he can do.”

Recent breakthroughs are so extraordinary that Joseph Jr. is aware of rumors that his formula for success may extend beyond hay, oats and water. He finds that regrettable.

“There is no other sport in the world where you have someone who is young and successful and you get negativity,” he said.

He insists that he has merely outworked many of the rivals who seek to disparage him. “It ticks me off because, with all of the work we put in, that is the way they are going to categorize us.”