NEW YORK—Elina Svitolina started her US Open campaign on Tuesday with a comfortable 6-3, 6-1 victory over Anna-Lena Friedsam, and then quickly settled into her post-match routine.

There’s the cooldown, stretches and treatment in order to get ready to do it all over again in two days. Before then, of course, there are numerous media and sponsor obligations to meet. But nowadays, part of Svitolina’s daily routine also involves a FaceTime call back home, as she checks in on daughter Skai from New York.

Svitolina and husband Gael Monfils, a former Top 10 player, have opened up about their choice to limit the 10-month-old’s travel at this early age—but that still doesn’t make it any easier to be apart.

“We decided for the sake of her health to leave her at home, unfortunately,” Svitolina revealed in her post-match press conference. “We miss her really much because this is like the last push now.

“It's been one month now that we didn't see her. We FaceTime every single day. But, yeah, it's not easy.”

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Q. How do you treat days off differently when you have her at a tournament versus when you don't?

ELINA SVITOLINA: Well, we had her at Roland Garros. Of course, we spend some time with her. But during the Slam, it is very limited time because all the time you wake up, you go train, you have treatments, you have media, you have everything, like so many things. Then in between her naps is managing your day, your time.

In the end I don't see her as much as I wish. So that's why we decided to leave her at home. We have a team who is taking care of her, as well, so she's super safe at home and watching some matches of us playing here in States.

Svitolina says she always has Skai on her mind, and before the match she shared a screenshot on Instagram of a FaceTime call with her daughter while on the way to compete at the US Open’s now-infamous Court 17.

“It's been one month now that we didn't see her," says Svitolina, pictured here with husband Monfils. "We FaceTime every single day. But, yeah, it's not easy.”

“It's been one month now that we didn't see her," says Svitolina, pictured here with husband Monfils. "We FaceTime every single day. But, yeah, it's not easy.”

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The Ukrainian has become one of the biggest storylines of the year after winning the title in Strasbourg and surging to a surprise semifinal result at Wimbledon, just months after returning from maternity leave. Svitolina, who reached the quarterfinals in Washington D.C., suffered an early exit in Montreal and had to miss Cincy due to injury—but is now back on track after Tuesday’s confidence-boosting result against Friedsam.

“Two weeks ago, it would be like a normal thing. But because I didn't play in Cincinnati and was a bit struggling with my health little bit, today this win and the form that I showed is a good day and a good win,” Svitolina said.

“But any win on the Grand Slam is a happy, happy day because the best players are here, everyone is there trying to beat you, trying to bring their best game. That's why there's so many exciting matches on the Grand Slam.”

No. 26 seed Svitolina will face Russia’s Anastasia Pavlyuchenkova in the second round.