SAN DIEGO — While the Dodgers resorted to a bullpen game against the San Diego Padres, Tuesday was a good day for their shadow starting rotation.

Shohei Ohtani threw 44 pitches to hitters in his third live batting practice session, moving a step closer to returning to two-way player status. Following that, left-hander Blake Snell threw 15 pitches in his first full-fledged bullpen session since April.

And in Los Angeles, right-hander Tyler Glasnow threw another bullpen session, moving forward in his return from shoulder inflammation.

The Dodgers still have 14 pitchers on the injured list, but Tuesday’s progress allowed them to start to see a light at the end of the tunnel.

“We are,” Dodgers manager Dave Roberts said. “There’s one side of it of just trying to focus on the guys that you have and keep moving forward. And the other part of it is the anticipation of guys coming back and becoming whole (as a pitching staff).

“Tyler threw today. Really encouraged with his bullpen in Los Angeles. Blake threw today here. Really encouraging. So, yeah, you can start to see us get to the other side. It’s stuff to look forward to.”

Ohtani’s latest step forward was delayed by three days due to weather and scheduling issues in St. Louis and his getting hit in the foot by a pitch on Saturday. He took the mound at Petco Park on Tuesday and threw three simulated innings against hitters imported from the rookie-level Arizona Complex League.

Ohtani dominated them, allowing just one ground ball up the middle that could be viewed as a base hit. His velocity held between 94 and 96 mph. The 44 pitches (including 23 in the third simulated inning) were a significant step forward from the 22 and 29 he threw in his first two sessions with hitters.

“He looks great. Things were coming out really clean,” Dodgers pitching coach Mark Prior said. “I think we’re gonna continue to build his volume. The intensity’s there, the pitches are there. I thought the execution was a lot better today than it was on his second one. This resembled more of his first live BP. So I think, all in all, he’s progressing and trending in a very positive direction.”

Prior said there are “ongoing discussions” about just how much buildup Ohtani will need before he is ready to pitch in actual games for the Dodgers.

“You start getting close to 44, you start getting into the 60- and 70-pitch range, then you can start envisioning and dreaming about being in a game,” Prior said. “Because then you know that he has the volume under him to go out there and at least take down multiple innings in a real game.”

Roberts put the chances of Ohtani making his Dodgers debut as a pitcher before the All-Star break optimistically at “north of zero.”

“It’s tempting. I’m sure Shohei feels tempted to just kind of rip the bandaid off and get into a big-league game,” Roberts said. “But I think we’re doing a good job of being patient. And truth be told, I don’t think anyone knows the right time to get him in a big-league game. We’re still being very careful, I guess.”

Meanwhile, Snell and Glasnow are finally making progress in their recovery from early-season shoulder issues. Snell’s bullpen session was his first since receiving a cortisone injection for his shoulder pain in late April. He made just two starts before going on the IL and said he didn’t feel pain-free until “probably two weeks ago.”

“For a while, I had no idea. It just hurt every time I threw a baseball,” he said. “I was kinda nervous, because I’ve never felt that. So I didn’t really know what was going on. And then like two weeks ago, I started to actually play catch with no pain. And I was like, wow. I started getting happy and excited.

“I think we can start moving. I don’t feel anything. All before that, every time I touched the baseball, the second I threw it, I could feel it. If it wasn’t the front, it was the back. If it wasn’t the back or the front, it was the side. It was just weird. I never felt that, even in my offseason. So I was just real confused. But now, very confident, feel great.”

Snell said he threw at about 70% intensity, all fastballs, Tuesday and looks forward to “pushing it” a little more in his next bullpen session, likely on Friday.

“Seeing Blake today live in front of us was great. His arm looks, for the first time probably all year, free and easy,” Prior said.

Glasnow’s session in Los Angeles was his third with an extended break when he experienced some back tightness following his first session off a mound. His velocity was 95-96 mph, Prior said. He could start facing hitters in live BP sessions soon.