None was closer than the final of the 50-over World Cup against England four years ago, when New Zealand missed out on boundary countback after two Super Overs failed to separate the teams.
The Black Caps accepted the Lord's defeat with admirable good grace, as they had far more emphatic losses to Australia in the 2015 title decider and the 2021 Twenty20 World Cup final.
Master batsman Williamson and strike bowlers Southee and Boult were key players in those three campaigns but, now approaching their mid-30s, their paths to India have been anything but smooth.
Coach Gary Stead has spent as much time sweating on medical reports as batting and bowling analysis this year, especially after totem Williamson ruptured knee ligaments in the Indian Premier League in April.
The New Zealand captain made a quite remarkable recovery to take his spot in the World Cup squad but only returned to batting in a warm-up victory over Pakistan on Friday.
Williamson will not be available for the tournament opener, a rematch of the 2019 final against England in Ahmedabad next Thursday.
"It was great to see Kane out there, albeit only with the bat today. He didn't feel it at all," he said after the match in Hyderabad.
"Pretty warming from a team perspective that we know he's pretty close to getting back to full fitness."
Southee's injury, a broken thumb which required five pins to repair, was more recent but, Stead said, the pacemen is confident he can play through the pain in New Zealand's second game, if not the first.
His strike partner Boult is fully fit and returns to the fold despite easing away from a central contract last year to take up lucrative opportunities in franchise Twenty20 cricket.
There is plenty of quality in the other 12 members of the squad, of course, although the loss of spin-bowling all-rounder Michael Bracewell to a ruptured Achilles in June was a major blow.
Stead placed his trust in the inexperienced Rachin Ravindra and Mark Chapman as well as bringing back the uncontracted Jimmy Neesham to try and fill the void left by Bracewell's absence.
New Zealand's coach knows it is a long tournament and said his team selections will be made on a match-by-match basis with conditions likely to vary from traditional slow Indian pitches to quicker surfaces that will suit pace.
The Black Caps have proved highly adept at tournament management in recent World Cups and Stead was unconcerned that they headed to India ranked sixth in the world.
"We've shown in the last month or so that we can beat England, which is one of the best teams in the world," he said.
"You don't have to beat them every day, you just have to beat them on certain days."
