However, the 18-year-old defender is now preparing for the biggest game of his life at the National Stadium after the Bairns were paired with Hibernian in the William Hill Scottish Cup semi-finals.
The former Spiders youth swapped Glasgow's southside for Falkirk's Westfield base last summer having never played a game for the Mount Florida outfit.
However, his promising form has been rewarded by new boss Steven Pressley and he is set to play a crucial part when the Irn-Bru First Division side face Hibs on either April 13 or 14.
He said: "I came up through the youth system at Queen's Park but I actually never had the chance to play for the first team.
"So my first game at Hampden will be against Hibs and it will definitely be the biggest game of my career so far.
"It was disappointing never to have made an appearance for Queen's Park's first-team but if you were giving me the choice of playing there for them or against Hibs in a Scottish Cup semi-final, I know which one I'd pick."
McGeever was happy to avoid Clydesdale Bank Premier League champions Celtic in the last four but so too did the skipper of their opponents, James McPake.
The Hibs captain said: "It's the best draw we could have hoped for.
"We have avoided the two SPL teams but I don't think Falkirk will be any easier because they are a league below us.
"They are in the semi-final on merit and are a good team. Their manager Steven Pressley is doing well there and it will be a tough game."
McPake was in the Easter Road side's line-up for last season's 5-1 final humiliation to Edinburgh rivals Hearts.
But he insists that while that defeat still hurts the remaining few players who suffered on that day, it will matter little to the rest of a much-changed Hibs team.
"At this club, there is always pressure to do well in this cup," he said. "It's been 111 years since we won it and last year didn't help.
"We didn't do ourselves justice and we want to get back. Not just because of last year, but also because it has been so long.
"There are only three or four of us still in the changing room from that game so it's not something we speak about. It's a whole new team, a new season, a different club now."
Dundee United were paired with Celtic in the second semi-final after coming through their derby clash with their city rivals from Dens Park yesterday.
Much of the build up to that game had surrounded Dundee's appointment of former defender John Brown as boss, but United chairman Steven Thompson hailed his own recent managerial appointment after Jackie McNamara steered the side to a 2-1 win.
He said: "Jackie is a young manager and he's ambitious. He wants to win things as all managers do.
"He'll hope to get to the final by beating his old team and I'm looking forward to the semi-final already."