April 12, 2018 04:55 PM

There’s no place like home for Khloe Kardashian.

The new mom, 33, who welcomed a baby girl in Cleveland on Thursday, is eager to get back to her home of Los Angeles after a tumultuous few days filled with cheating allegations against her boyfriend, Tristan Thompson, 27, leading up to the delivery.

“The goal is to get Khloé out of there as fast as they can without jeopardizing the safety of the baby after she’s arrived,” a source told PEOPLE before the birth. “Khloé just wants to be home.”

But how soon can she and her little one safely get out of Cleveland?

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“Typically, the earliest you can fly with a newborn is when they’re two days old,” says Tracy Stewart, an air travel expert and editor at Airfare Watchdog. He notes, some commercial airlines insist on waiting until a newborn is two weeks.

Khloe, whose mom, Kris Jenner, 62, and sister, Kim Kardashian West, 37, flew out on private jets to be by her side at the hospital, sources confirm to PEOPLE, plans to return with them the same way. Flying private allows her to avoid many typical regulations.

“For private, it’s probably closer to two days,” says Stewart. “That being said, there’s a risk of blood clots for the mother when flying so soon after delivery.” He adds ideally, “It’s best to wait at least six weeks.”

If waiting isn’t an option, Stewart notes, “new mothers are encouraged to drink plenty of water and stay hydrated” while flying. “It’s also a good idea to wear special circulation socks or hose” that help prevent blood clots.

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On Tuesday, photos and videos surfaced of Thompson, with whom Khloe has been living in Cleveland, where he plays for the Cavaliers, allegedly getting close to an unidentified woman at an N.Y.C. lounge over the weekend. TMZ also posted footage recorded in October 2017 allegedly depicting Thompson kissing one woman while a different woman groped him at the Darna hookah lounge outside of Washington D.C.

Khloe stayed strong as the scandal broke, and even let Thompson bond with their baby after the birth, choosing to be “the bigger person,” according to a Keeping Up with the Kardashians source.

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But heading back to L.A. early amid the heart-wrenching news may never have been an option for the heavily pregnant star.

“Most, if not all, commercial airlines won’t allow pregnant passengers to fly after 36 or 37 weeks,” says Stewart, and “Private jets typically follow the same guidelines, restricting travel after 36 weeks, with a medical certificate required after 28 weeks.”

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He adds, that “private jets are definitely known to be a little more flexible if a passenger has a doctor’s letter of approval.”

Khloé had always intended to raise her little one in Cleveland, where she and Thompson have been nesting for the last year, a source tells PEOPLE, but that plan has now changed as Khloe prepares for her imminent return to L.A.

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