The switch to ground-effect cars last year heralded a lean period for Hamilton and Mercedes, with the seven-time world champion going without a win since 2021 and having to wait 33 races before qualifying on pole again.
Having ended Friday's practice session with his car feeling "at its worst", Hamilton topped FP3 on Saturday morning before going on to beat Max Verstappen by 0.003 seconds on his final lap of Q3 to claim his 104th career pole.
Speaking in parc ferme after qualifying, Hamilton admitted he "didn't expect" to be in contention for pole and had "nothing left in it" come the end of the lap.
"It's been a crazy year and a half," Hamilton began.
"So, I've lost my voice from shouting so much in the car. It's amazing, that feeling. I feel so grateful to be up here because the team have worked so hard.
"We've been pushing so hard over this time to finally get a pole, it just feels like the first time.
"And a big, big thanks to the crowd here. We have such an amazing crowd every year here in Budapest.
"I didn't expect coming today that we would be fighting for pole. So, when I went into that last run, I gave it absolutely everything. There was nothing left in it."
Hamilton added that the previous year and a half have been "challenging for every single person in the team" and concedes that the "tough times" will continue beyond Hungary.
"There's been ups and downs, it's a big, big roller coaster ride," he said.
"But none of us have lost faith. We've all just united together. We're focusing on trying to steer the car into that direction.
"Today, we were losing time in Turn 4 and 11 compared to the others, so I just sent it and hope that I stayed on track.
"But it has been tough. And it's going to continue to be tough moving on from here.
"But I think hopefully this shows that we're on the right track. And we can do it if we just keep pushing."
Despite the pole, Hamilton has remained grounded in his hopes of ending his victory drought on Sunday, noting: "I think tomorrow we'll just study as hard as we can.
"We'll bring our A game tomorrow as a team. It's gonna be difficult to fight these two guys [Verstappen and third-placed Lando Norris].
"Lando has been doing a mega job, it's been great to see McLaren up there battling and Max, he's always up there, he's always doing his thing."
