THE PARENT: Desiree Toneatto, 44, of Doylestown

THE CHILD: Kai Erik, 6 months, adopted October 16, 2018

HIS NAME: Desiree always loved the name “Kai,” which means “pier of a harbor” in Basque. “Erik” is for a colleague’s son who died at age 37. “It’s so we won’t forget him,” she says.

After a brief, childless marriage, three IVF cycles, two early miscarriages, and two adoption attempts that never came to fruition, the only remaining obstacle between Desiree and parenthood was a ruptured tire somewhere in the Arizona desert.

She and her mother had lit out from the East Coast — more than 30 hours of nonstop driving — as soon as Desiree got the call from A Baby Step Adoption: “She’s in the hospital. The baby’s going to be born tomorrow.”

The car was packed with a month’s worth of clothing, a car seat, diapers, boxes of organic, sugar-free formula, and a portable crib. Tumbleweeds swirled across the empty road. Phoenix, and the hospital, and her son, were still 250 miles away. She’d been waiting for nearly a year.

Actually, she’d been waiting her whole life. Desiree, the only child of parents who spoke fluent Italian and German, was born in an Army hospital in Italy. In elementary school, when her father taught at West Point, she was the kid who wheeled other people’s babies around the campus in their strollers.

Later, Desiree’s home became kid headquarters, a place where friends were always welcome. Her mother stirred up a different kind of spaghetti sauce each week. “I always thought I would be a parent. I thought I would have four children,” she says.

But as she grew older — becoming a figure skater, a student of biology and chemistry, a middle-school teacher of German — even one child proved elusive. A decade ago, she was married for less than a year; she and her husband lived 60 miles apart and never shared a home. “The distance was too great, and neither one of us could give up our jobs,” she says.

She tried a matchmaker but didn’t find her soulmate. She attempted to conceive on her own, with the aid of fertility specialists and donor sperm; twice, her pregnancies ended in early miscarriages.

In 2015, she proudly told her students she’d won the Outstanding German Educator Award from the American Association of Teachers of German. “One girl said, ‘Wait a minute. You don’t even have any children.’ Then a boy said, ‘You can adopt me!’ That resonated. It hit home. That’s how I decided to adopt.”

She liked the intimacy and warmth of A Baby Step Adoption; by August, she began submitting her profile book to birth mothers whose situations she read about in the agency’s weekly e-mails. After two months, she was matched with a birth mother in Florida. Desiree met the woman for coffee and felt her hopes lift; after the birth, though, the mother decided she would raise the child with her boyfriend.

After a second match turned out to be a scam — a woman demanding money but who had no intention of relinquishing her baby for adoption — Desiree was wary but resolute. “I was just never going to give up,” she says. “There’s a reason I’m here. We come through life only once. I knew I would be a good mother to a child.”

In May, after a call from A Baby Step, Desiree talked via FaceTime with an Arizona woman who was nearly eight months pregnant. “We both cried,” she remembers. “We talked about everything. We had conversations about hopes and dreams for the child. She said I reminded her of her best friend. It was a good moment, but in the back of my mind, I was thinking: I hope this goes through.”

Desiree launched into action: the baby’s room, decorated in gray and white. Substitute-teacher guidelines for her middle-schoolers in case she had to leave before the end of the year. A plan with her mother, who lives with her, to care for the baby once she returned to work.

But she didn’t anticipate a blown tire on the edge of Arizona. Thanks to a rented Jeep Cherokee, they made it to the hospital six hours after Kai was born. Desiree, following the birth mom’s wishes, cuddled him skin-to-skin. “He looked like the grandfather I never met,” she remembers. The birth mother, still tethered to an IV pouch, brought orange roses to Desiree’s room.

“I looked at her and said, ‘You’re the best person in my whole life. Because of you, my whole life is changing.’ ”

They spent a month in Phoenix, living in an apartment owned by a friend of a retired colleague. Every day, Desiree and her mother took the baby out for walks. “We were in a nest, bonding and cuddling, establishing a relationship with this new child: What are his needs? What does he like?”

The trip home was slower: overnight stops at Holiday Inn Express motels in Santa Rosa, Tulsa, and St. Louis; take-out from McDonald’s, where workers gushed over the infant. It was an echo of what Desiree learned as a child, bouncing from Italy to Texas to West Point to Philadelphia: The world is surprisingly small. People are genuine. Making friends grows easier with practice.

At home, Kai was wide-eyed as Desiree carried him from room to room. “This is your house,” she told him. “This is your yard.” She writes to Kai’s birth mother every three months. “He will always know the truth, that he was adopted,” she says. “That his first mom, his birth mom, loves him as much as I do; she just couldn’t care for him.”

Kai seems to soak up details of his surroundings; he babbles at everyone. His grandmother sings to him in German. His mother cuddles him after he gets a shot.

“Whenever he cries or is upset and I pick him up, he stops. As soon as I put him on my shoulder, he stops crying. Or when he hears a loud noise and gets scared, I pick him up and he’s totally OK. That’s when I know: I’m his person, and he’s my person. He’s my kid.”