Fresh from a week's recovery after their series-saving 26-10 win over South Africa, Cane said the squad had quickly settled into their pre-Test routine with the goal of continuing the growth in their game.
"We'd been saying for a couple of weeks we'd been improving and took a significant step in that game. It's a performance we're proud of, for sure, but it's just a start of where we want to get to and how we want to get better.
"It's one performance. Just because we got that one right doesn't guarantee we get this one, so there's plenty of work to go in this week. For us, it's a good stepping stone."
Cane felt the All Blacks possibly took it for granted when visiting South Africa twice a year during Super Rugby and the Rugby Championship before 2020. But it had been nice to go back and spend two weeks there to get closer as a group.
"I'm proud of how we stuck tight and focused on what's important and kept chipping away at our work."
While there had been a resolution to the coaching situation, Cane said nothing changed. They reviewed the South African game as they always did. Then it was back to work.
"It's pretty exciting to be back in Christchurch after six years since we had a Test match here. It's been a long time.
"I've played the Pumas a fair few times. They're one of the best defensive sides in the world when they get it right. They're very hard to attack against, and they cause us trouble at the breakdown.
"If we don't kick well, or have a good chase line, they can spread the ball well. They've got some exciting backs with exceptional footwork, so we've been doing our homework on them for sure."
"One thing we know about the Pumas is they will turn up with plenty of passion and [will] play with plenty of emotion and throw everything at you. We're aware of that and will make sure we match that, and play with physicality and intensity, if not more.
"A few years ago we got dragged into off-the-ball stuff so it's important we stay task-focused."
He was not surprised by Argentina's record win over Australia. Having played them so often in recent years, the All Blacks knew they had many quality players.
Pablo Matera, who played for the Crusaders earlier in the year, would look forward to this Test as a second homecoming.
"He's a special player, heck of an athlete. He's pretty much got it all in terms of a loose forward and, although he's not their captain any more, he's a bit of a figure as a leader within their squad. He's consistently played some of his best footy against the All Blacks. so we'll do our best to stop him."
Former Ireland coach Joe Schmidt got into his work quickly. Having him on a full-time basis was a privilege, Cane said.
"He's already stamped his mark in a couple of areas. He'll be predominantly looking after attack, and attack structure. We've had a few sessions in the classroom with him already."