The Hendrick Motorsports machine was almost four seconds faster than the quickest GTE Am entry in Wednesday's opening qualifying session, despite the team's modest pre-event public predictions of being somewhere in the middle of the GTE Am pack.
Instead, 2010 Le Mans winner Mike Rockenfeller posted a 3m47.976s lap that was only 8.5s slower than the lowest-ranked of the LMP2s.
"I think we've progressed a lot and here we are qualifying four seconds quicker than all the GTE cars - I think it's a phenomenal effort by the whole team," said Button.
"We came here thinking we'd be in the mix and, when the GTE cars get the amateur drivers in the car, we'd be able to be as quick as them - if not quicker - but we didn't expect to qualify four seconds in front of the quickest GTE car.
"Everything has been spot on, all the homework that's been done by this team has been phenomenal and I would put it up there with one of the best teams I've raced with in the world."
Rockenfeller said fast lap times had been simulated before arriving at Le Mans, but he still feels the qualifying performance was better than expected.
"When we started with the Cup car we felt there's so much potential and then we tweaked it and got faster and faster at Le Mans on the sim, but you never know until you hit the real track," he said.
"To be here now, having qualifying done faster than we expected on the sim, everybody can be so proud - so far we have overachieved."
However, Button has cautioned that finishing ahead of the GTE Am runners will likely be more difficult in the race.
He explained that multiple factors, including possible rain showers predicted for this weekend's event, are likely to contribute to a closer contest.
"We'll have to change brakes during the race, which takes us five minutes - for the other guys it's one minute - so that's over a lap," added Button.
"The goal has to be to beat the GTs. First of all to finish, and then to finish in front of the GTs. And, if we can do that, it's a great achievement."
The 2009 F1 champion, whose only previous Le Mans outing came in 2018 with SMP Racing with a BR Engineering BR1, also stated how much he was enjoying driving the NASCAR machine.
"I love the sound, I love the look, I love the challenge - and this is a real challenge, to take a Cup car base and to build it into something as quick as Hendrick Motorsport have is really impressive," he said.
