A season that began with no new signings and the club's one billion pound stadium project running late, now has the potential to climax in Madrid with the club's first-ever appearance in the final of Europe's blue-riband tournament.
There is still a long way to go, with a young Ajax side sure to present a formidable obstacle to a Spurs squad shorn of leading strikers Harry Kane and Son Heung-min.
But Pochettino says his side must aim for the moon.
"I'm living my dream. I have already lived my dream. Five years ago (when I arrived) to be in the semi-finals with Tottenham was a dream," he told reporters at the club's training complex north of London on Monday.
"When you dream you must dream with the moon. You have to set your dreams at infinity and beyond.
"If you put your dreams down here (indicates with hands), it's like a bottle without water."
With club talisman Kane still out with an ankle injury he sustained in the quarter-finals and Son suspended, the circumstances are not ideal for Tottenham as they approach their first European Cup semi-final since losing to Benfica 1962.
They are also without Harry Winks, who had groin surgery on Monday, and Erik Lamela and looked fatigued in a 1-0 Premier League defeat by West Ham United on Saturday -- their first defeat in five matches at their new stadium.
Eredivisie leaders Ajax, by contrast, had a weekend off but Pochettino is not one to seek excuses.
"The chance to play a semi-final for Tottenham doesn't happen often," said Pochettino, who is yet to win a trophy in five years at Tottenham.
"The circumstances are impossible to change. It's impossible to be tired, impossible not to be excited. I've got no doubt we have the energy."
Tottenham, aiming for a first European final since the 1984 UEFA Cup when they beat Anderlecht on penalties, are at full-stretch for the visit of the four-time kings of Europe.
But Pochettino brushed off suggestions that a 0-0 draw might be a good outcome on Tuesday against a vibrant young side that has already knocked out Real Madrid and Juventus.
"I'm so optimistic. We are thinking that we can win the game," the Argentine, who hopes to have midfield powerhouse Moussa Sissoko back from a groin strain, said.
"How we arrived here is because we are a collective. We are limited (in options) but we have huge optimism. To play a Champions League semi-final in our new stadium is something no one believed a few months ago."
(Reporting by Martyn Herman; Editing by Christian Radnedge and Ken Ferris)
