The award-winning band is celebrated in Country Music Hall of Fame and Museum exhibit that runs through June 2019

You’re sure to do a double-take when you see what’s printed on this concert ticket: “Keith Urban with Little Big Foot.”

Whoa. So much for name recognition.

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That 2004 ticket, now on display in Little Big Town‘s new exhibit at the Country Music Hall of Fame and Museum, puts in a nutshell the quartet’s long and difficult climb to the upper echelons of the genre.

As band member Karen Fairchild, 48, says: “That, right there, is really the story of our lives.”

There were other infamous miscues of the now familiar name: “Little Big Horn” and “Little Big Toe” were two that bandmate Phillip Sweet, 44, remembered during a public event at the Nashville museum this week to celebrate the opening of the exhibit, “The Power of Four.”

Image zoom Keith Urban and “Little Big Foot” Nancy Kruh

Getting their name right, though, was hardly their biggest problem starting out. Formed in 1998, LBT endured seven years of struggle — including two disastrous drops from records labels — before the band earned their first Top 10 single with “Boondocks.” That 2005 hit marks the moment when Fairchild, Sweet, Kimberly Schlapman, 48, and Jimi Westbrook, 46, finally found their musical groove.

Still, it would be another seven years, in 2012, before they were able to break through with their career-making hit, “Pontoon.” Since then the band has gone on to earn shelves of Grammys, CMAs and ACMs, as well as multiple No. 1 songs and platinum albums.

“I believe — we all believe — were it not for our journey, we would not be this band,” Schlapman told a crowd of several hundred family and friends at a museum reception. “We’d be a different band if it had been smooth sailing the whole time. We’d be different people. And we are grateful for every bump in the road, every low, every high. And we celebrate the highs and appreciate them more because of that journey.”

Image zoom Phillip Sweet, Karen Fairchild, Kimberly Schlapman and Jimi Westbrook of Little Big Town Jason Kempin/Getty

Even after 20 years together, the four artists still marvel at the memory of the first time their voices merged during Sweet’s living-room tryout. He was the final jigsaw puzzle piece for the group, which was the brainchild of Alabama college pals Fairchild and Schlapman. (Westbrook signed on several months before.)

“When we heard the blend, we felt like that’s what we’ve been looking for,” Westbrook, who later married Fairchild, recalled to PEOPLE.

“It was kind of a spiritual experience,” Sweet said. “We all lit up.”

But the sound wasn’t all they were seeking, Fairchild added. “We also knew the chemistry off stage had to be as important as the chemistry of the voices,” she said. Thankfully, she added, “we could tell it felt like home from the very beginning.”

Their harmony, both on stage and off, is the thread that runs through the entire museum exhibit, an expansive display of LBT stage wear, couture and artifacts. Highlights include Fairchild’s high school cheerleading uniform (complete with pom-poms), their 2015 Grammy for “Girl Crush,” and the neon “Pain Killer” sign featured on the cover of their 2014 album with the same name.

Image zoom Karen Fairchild’s cheerleading outfit Nancy Kruh

But perhaps the most precious and unusual memento comes from one of their most famous fans, Taylor Swift. Of course, she was the songwriter behind LBT’s 2017 #1 single, “Better Man” – but that wasn’t the first thing the country-turned-pop superstar wrote for the quartet.

While working to complete high school, Swift chose the band as the subject for an English assignment. She presented them with a copy of the essay, in a leather binder, at a private party celebrating the 2006 gold certification of their album The Road to Here.

Image zoom Taylor Swift’s essay Nancy Kruh

“I was supposed to do a term paper for my English credit this year,” Swift wrote in her cover letter to the group, “and I was supposed to choose a topic for it that I was interested in and intrigued by. Well, I chose you. I thought you’d find that pretty amusing. Ha. Here’s a copy. I love you guys!”

The actual essay is hidden from view in the exhibit, but Fairchild assures, “Well, you know her. It’s good!” The title, Fairchild added, is “The Little Band That Could.”

Image zoom Jimi Westbrook, Karen Fairchild, Kimberly Schlapman and Philip Sweet of Little Big Town Jason Kempin/Getty

And LBT is still the little band that can: The foursome is now hitting the road, co-headlining with Miranda Lambert, on a summer “Bandwagon” tour. The show will feature performances with all five artists on stage.

“Jimi and I are just trying to hold on to all the girl power that’s happening in this show,” Sweet said. “It’s amazing.”