New Zealand are attempting to make history by winning a third successive Rugby World Cup title, but Jones sees Saturday's semi-final clash in Yokohama as an opportunity for England to cause a major upset.
He believes the talent that convinced him to take the job is starting to shine, as the 40-16 last-eight win over Australia proved.
"I saw a team that could be great and that was the challenge, and they are starting to believe it," Jones said.
"We have a challenge this week because we are playing the greatest team that has ever been in sport. If you look at their record, no other team has that over a sustained period of time.
"So we are going to have to be better, improving, and see what we can get out of this week's preparation. New Zealand are a great team with a great coach and great captain, but like any team they are beatable and we will be investigating every possible way of how we beat them this week.
"You always want to play the best and they are the best, no one can dispute that. For the players and coaches this is the best week of their lives. You have to enjoy it, and make sure you focus on yourself and work to get better."
So what convinced Jones that England were a sleeping rugby giant he could awaken?
"The age profile, the talent of players. What is top sport about? You've got to have talent to get in the front door. But then you've got to have a work ethic, you've got to be relentless. You've got to put the team ahead of the individual. That's the coaching part.
"When you're a national team coach, it's about luck isn't it, because you don't develop the talent. You don't know what's going to be out there.
"There was talent here (in 2015) but like any team, you need to learn about how you work as a team. It's not easy. Most people don't want to do it."
Jones believes the win over Australia, based on a huge defensive effort, showed his England players are yet to reach their peak.
They're a strong team and they're getting stronger all the time. They're believing in each other, they believe in the way they play. I've got a massive admiration for the way they've prepared for this World Cup.
"Look at the second-half score (against Australia), was it 23-7? That doesn't come from blowing magic dust, it comes from working hard.
"We have had no player playing in a World Cup semi-final. We know with a semi-final the whole sporting world is looking on. It is a fantastic thing to be involved in - and with only four who (had) played in a quarter-final - it's a great opportunity for us to do something different."
England came close to beating New Zealand at Twickenham last year with a late try controversially ruled out when Courtney Lawes was penalised for being offside as he charged down a kick, from which Sam Underhill crossed. England lost 16-15.
"I think both teams have moved on and we have seen at this World Cup that what has happened in the past is irrelevant. We are in a World Cup in a neutral country - referees, crowd, atmosphere - and the teams that adapt are the ones making it to the end of the competition."