THE PARENTS: Taryn Stinson, 44, and Matt Burlick, 40, of Fishtown

THE CHILDREN: Grayson Walter and Jackson Austin, 9 months, adopted June 25, 2020

THE NAMES: They used an app in which both partners can swipe left or right, then share their favorite picks. The middle names are from beloved grandfathers, and they wanted first names that could be shortened: Gray and Jax.

It was a 10-mile hike to the top of Mount Tamalpais in Marin County. Matt had the ring in his pocket; he’d already encouraged Taryn to wear something more photogenic than yoga pants and a random shirt.

But halfway up, Matt realized he couldn’t wait. He asked. She said yes. And then, in typical Taryn style, she insisted they finish what they’d started and trek to the summit, where a cell tower would enable them to capture the moment on their phones.

Taryn’s ambition and drive were no secret; in fact, that was part of the attraction when the two first met — a chance encounter while she was walking in downtown Hoboken with Matt’s cousin, who happened to be Taryn’s best friend.

They chatted briefly outside a cafe. And when the women left, Matt texted his cousin: “Who’s your friend? I’m interested.”

She was drawn to his curiosity — he’s a professor of computer science and machine learning — and his prowess on bass guitar. He was struck by her relentless work ethic, even when at play; during a scavenger hunt in Hoboken, “she was an absolute madwoman, running around like Wily Coyote,” he says.

Their engagement came in the middle of a three-year stint of living apart — Taryn in San Francisco, working in sales management for Johnson & Johnson, and Matt living with relatives in Kearny and working toward a Ph.D. in computer science. They dated remotely, each cuing up the same movie on their iPads and discussing it afterward over take-out.

They married in Tulum, Mexico, a frequent destination for Taryn’s family while she was growing up in Houston. Guests stayed in beachside villas and toured Mayan ruins; Taryn’s parents arranged a surprise visit from a mariachi band.

And in the midst of wedding planning, Taryn accepted a new job in Philadelphia. A week after they said “I do,” she packed her belongings and flew east; together, they rented a place in Bella Vista.

“I’ve been very career-driven most of my life, and Matt followed me around,” Taryn says. Her feeling about children was, “OK, I’ll take care of that later.” Matt felt the same way: “I was trying to finish up my Ph.D. and get that done so I could establish a career and get settled.”

Taryn was 40 when “later” became “now.” Though she’d thought about adoption ever since watching a television special about Operation Babylift — the evacuation of babies and children from South Vietnam in 1975 — Matt wanted to try conceiving first.

“We harvested my eggs, and they weren’t great. I call them raisins,” Taryn says. So they chose an egg donor and began what turned into a three-year saga of IVF transfers, a miscarriage, a possible ectopic pregnancy, and the removal of both of Taryn’s fallopian tubes.

“Getting pregnant was never super-important to me, but once I commit to doing something, I want to see it through,” she says. For Matt, those years were “frustrating and upsetting. As the male, you’re kind of a bystander, a little bit helpless. All you can do is try to give emotional support.”

By the time of the fourth and final embryo transfer, they’d decided to pursue adoption simultaneously. “I was scared to go through the process,” Taryn recalls. “Was I setting myself up for more disappointment?”

But once they began working with A Baby Step Adoption, she embraced every step as a new challenge: the dozens of essay questions that called for thoughtful responses; the profile book that required them to sum up their existence in a handful of photos and 200 words. “I realized how much I care for Matt; it made me appreciate the things in my life. I felt like our marriage got stronger because I had to do a lot of self-reflection.”

Throughout the spring and summer of 2019, they read descriptions of birth mothers emailed to them by the agency. It took six months to match: a woman who was four months pregnant and living in Arizona; she hadn’t had an ultrasound yet, so didn’t know the baby’s sex.

Taryn and Matt were in Florida for Thanksgiving when the caseworker called: The ultrasound showed a healthy baby. Actually, two babies — fraternal twin boys. “Are you still interested?” the caseworker asked. They were.

The birth mother was due in March, but her water broke in late January; she was admitted to the hospital and given a magnesium drip to slow her contractions. Taryn and Matt flew to Arizona; the next day, they were escorted to the NICU to meet their sons.

“I felt like I was in a dream,” Taryn recalls. “Like I was watching somebody else’s life.” The babies were small — under four pounds each — but healthy. And the NICU nurses became parenting coaches, teaching the couple how to feed, diaper, and soothe their infants.

Jackson left the NICU after a month; his brother needed one more week. It took another week to get clearance to take the infants out of state. “This was on the cusp of COVID,” Matt says. “We were a little bit nervous.” He recalls the fiasco at the airport gate as he struggled to fold a stroller and juggle bags and babies while a nearby passenger chuckled at the scene.

The twins slept soundly all the way home — Philadelphia, Fishtown, their bassinets in a room Taryn had hand-painted with a mountain scene. “To me, that was one of the landmarks,” Matt says. “Before, it felt like a dream or a vacation: let’s role-play being parents in some foreign city.”

Now it’s real: Jax’s goofy smile, Grayson’s full-out giggle, the blessing and struggle of running Mommy & Daddy Daycare while also working from home. “The first year of their lives, I’m going to see every moment,” Taryn says. “I think parenthood has given me the ability to slow down a bit, which is probably what I needed anyway.”