LOS ANGELES — There might not be a bigger question in the MLB season’s second half than the health of Dodgers prized free-agent acquisition Yoshinobu Yamamoto. The Dodgers’ $325 million man has been sidelined by a strained right rotator cuff since June 15, and while the injury isn’t believed to be season-ending, according to the team, the rehab and recovery have already taken some time.

Speaking Sunday for the first time since mid-June, Yamamoto discussed his latest steps on the journey back from the shoulder injury.

“I have started throwing [again],” he said. “And day-by-day, extending range, distance and velo, too.”

Prior to the injury, Yamamoto had begun to show why the Dodgers were so determined to sign him last offseason. The Japanese right-hander is 6-2 with a 2.92 ERA this season, and he owned a 2.39 ERA in his last five starts before the injury.

“He’s going to be stretching it out to close to 200 feet,” manager Dave Roberts said of the next steps. “So it’s a pretty good distance. I don’t have a timeline on when he’s going to throw a ‘pen, but he’s pain-free right now.”

A few weeks ago, the Dodgers moved the rookie right-hander to the 60-day injured list, and he was shut down from his throwing program. He is now eligible to come off the IL in mid-August, but Los Angeles won’t rush the young righty back, especially not with so much invested in him over the next 12 years.

That said, Yamamoto confirmed Sunday that there has been no pain or discomfort in his shoulder while throwing and that he would like to return to the team’s rotation at some point this season.

“That’s my goal,” he said. “I’m trying to come back as soon as I can.”

Added Roberts: “I think it’s just one of those things that you want to do the best for Yoshinobu and make sure that he’s healthy now and also in the long term. That’s the priority.”

Starting pitching was a major question for the Dodgers going into this season, and with so many injuries to the likes of Yamamoto, Walker Buheler, Tyler Glasnow, Clayton Kershaw and more, that question has only gotten bigger as the season has progressed. The rotation will get some relief with Glasnow returning from the IL on Wednesday and Kershaw set to make his season debut Thursday. But there should still be concerns about the team’s durability down the stretch.

Next week’s trade deadline certainly offers president of baseball operations Andrew Friedman and the Dodgers’ front office an opportunity to bolster the rotation. And if there’s one thing we know about Friedman, it’s that he’ll be looking for any way to improve his team’s chances in October.

“This is probably one of the tougher [trade deadlines] that our front office has to deal with,” Roberts said. “Because of the amount of guys we’ve had on the IL, impact guys. … [We’re] really trying to have conversations with the players, with the training staff and trying to figure out who’s going to come back, who can we bet on coming back and who is 50/50.

“This is a tricky one. But we’re evaluating every day, and guys are trying to get better. So the guys we have now are getting opportunities, so there’s a lot of evaluation on the field and off the field.”