The defender has played – and scored – for his country at the national stadium but a cup run at first-team level has eluded him.
Killie host Aberdeen in a William Hill Scottish Cup fifth-round replay on Wednesday night two years on from bowing out on penalties against the Dons at the quarter-final stage.
"That was probably one of our biggest disappointments, that we didn't get a chance to go to Hampden, because we were on a really good run of form back then and had two really hard-fought matches against Aberdeen," Findlay said.
"It's not something we are looking to rectify because of that, it's just an aim to get as far as we can in the cup and it's a really good opportunity now we are at home to get ourselves into the quarter-finals."
Findlay has suffered replay defeats against Rangers in each of his other two Scottish Cup campaigns at Killie and the 24-year-old pines for a run to the latter stages.
"I've got a wee bit of experience playing in youth finals but it's something I am definitely missing myself," the former Celtic academy player said.
"I have never had a realistic look at getting far in a competition. Not just personally, it's something everyone in the changing room would love to be able to do – get as far as we can. We just need to go out and give ourselves that chance to get one step closer.
"It's a dream of every player to lift a cup in a national final, to win trophies.
"We have a squad that can go far. If it's the luck of the draw, you need to just win the right game at the right time.
"It's just something we have not managed to do, to get ourselves in a position to go to Hampden yet. It's an ambition that we all share."
Killie have shown they have a team capable of beating the best in Scotland on their day. They have secured two victories and two draws against Celtic and five wins and four draws against Rangers since Steve Clarke and current manager Alex Dyer arrived in October 2017.
But the form that has earned them two record points tallies in the league has so far not translated into cup success.
"Obviously the league is the most important and what we have done in the league in the last two seasons is amazing," Findlay said. "And to get into the top six is still the first aim this season.
"But when you are in a cup competition, no matter who the opposition is and what the cup is, you want to win and get as far as you can.
"Any team at home, we fancy ourselves to go out and win the game."