The Yankees are accustomed to getting what they want. But they didn’t land Mr. Ohtani or Mr. Yamamoto.

Los Angeles Dodgers relief pitcher Yoshinobu Yamamoto, left, and designated hitter Shohei Ohtani sit in the dugout during the fourth inning of a spring training baseball game. AP/Ashley Landis

Los Angeles Dodgers slugger Shohei Ohtani uncorked a mighty swing in the fourth inning of his first spring training game this week in Glendale, Ariz. The smash in his third at-bat sent the baseball sailing over the left-field wall and delivered a message to future rivals like the New York Yankees.

The two-run home run in an eventual 9-6 Dodgers victory over the Chicago White Sox doesn’t count. But his Cactus League debut reinforces the notion that teams expecting to win a World Series may need to go through the talent-laden Dodgers.

“It was definitely, a big first step,” Mr. Ohtani told reporters in Arizona through an interpreter. “The big thing for me was that I was able to finish off the game without any problems.”

Mr. Ohtani, a two-time American League Most Valuable Player, signed a 10-year $700 million contract to join the Dodgers after six impressive seasons with the Los Angeles Angels. The Dodgers later added a highly sought-after Japanese pitcher, Yoshinobu Yamamoto, for $325 million over 12 years. Their additions are why the Dodgers are the betting favorite on FanDuel to win the 2024 World Series.

Mr. Ohtani’s home run may not have counted, but it should serve as a reminder to teams like the Yankees, who may need to strengthen their rosters should they meet the Dodgers in the post-season.

Yes, that’s a long way away. The Yankees are first concerned about American League contenders like Toronto, Tampa Bay, Minnesota, Cleveland, Houston, and the defending champion, Texas Rangers. But there’s a growing urgency for the Yankees to solidify and dominate their rotation by signing free-agent pitcher Blake Snell while they can.

Mr. Snell, a Cy Young winner in both leagues, remains available, looking for a deal in the $30 million-per-year range.  For the Yankees, it’s a hefty price tag to add to a payroll already at around $300 million.

Negotiations are ongoing, though nothing appears imminent to sign Mr. Snell and strengthen a rotation that already includes 2023 American League Cy Young Winner Gerrit Cole and two-time All-Star Marcus Stroman.

Owner Hal Steinbrenner made clear at the opening of spring training that winning a World Series is the only goal, and said the Yankees aren’t finished trying to improve their current roster.

“I think we have a championship-caliber team right now, but we haven’t stopped looking to improve and we never will,” Mr. Steinbrenner said at Tampa. “We’re able to do whatever, we’re able to do all the way up to the trade deadline. We continue to look at a lot of different options. Given where we are payroll-wise, any addition to the club is going to be a costly one. But I’m still willing to consider anything that comes my way.”

The Yankees look healthy and stacked. New acquisition Juan Soto belted a home run in his spring debut. Mr. Soto teams with a healthy Aaron Judge and a rejuvenated Giancarlo Stanton to anchor what the Yankees hope will be one of the most potent offenses in the major leagues.

But will the Yankees have enough dominating pitching to make the playoffs and ultimately earn the franchise’s 28th World Series championship — its first since 2009?  Mr. Cole had his best season last year, but the Yankees finished 82-80 and didn’t make the playoffs. Not being able to compete for a World Series made for a bittersweet season.

“It’s the main reason why I’m here,” Mr. Cole said recently. “The Yankees and the Steinbrenner family and us as an organization, we set out to do that every year and they provide us the opportunity to reach that goal. You don’t take that for granted and it’s at the forefront of your mind when you’re preparing.”

Mr. Cole welcomes the addition of Mr. Stroman, who is 77-76 with a 3.65 ERA for his career. He was voted to the All-Star team last year with the Chicago Cubs but declined to rest.

“He’s always thinking out there and he’s one of the fiercest competitors that we have in this game,” Mr. Cole said. “His level of consistency throughout his career speaks to how good of a professional he is and how talented he is.”

The Yankees are accustomed to getting what they want. But they didn’t land Mr. Ohtani or Mr. Yamamoto. With the Dodgers already flexing their muscles, the Yankees might move to land Snell while they can.