But none of the current squad has played a test match in Perth, Melbourne or Sydney venues for the series and until they do so, and succeed, it is unlikely they will be able to wear that laurel.
New Zealand has won only one test series in Australia in 1985 when Richard Hadlee and Martin Crowe helped secure that historic achievement. It has won only one of 22 Tests in Australia in the intervening 32 years and overall has won just three of 31 Tests on Australian soil.
Australia won the last test series between the teams in Australia 2-0 in 2015 and the last series in New Zealand 2-0 in 2016.
In one of its most important summers, New Zealand will follow the series in Australia with a home series against No. 1-ranked India. If it wins both series it will pass India to claim the No. 1 ranking for the first time.
But that is tough, perhaps even unthinkable. Australia is in superb form after sweeping Pakistan 2-0, led by the record-breaking batting performances of David Warner and Marnus Labuschagne and the bowling of Mitchell Starc, Pat Cummins and Josh Hazlewood.
New Zealand's inexperience in Australian conditions is perhaps its greatest handicap. It has had no warm-up in those conditions ahead of the first test which will likely be played on a fast and bouncy pitch at the new Perth Stadium, and it has little recent experience of day-night cricket ahead of the pink ball series opener.
It will also face unfamiliar heat: temperatures are expected to touch 40 degree Celsius (104 F) on some days in Perth before cooling in the evening.
The other Test venues are also new to the Kiwis: New Zealand will play the Boxing Day test on a pitch of unknown quality at the Melbourne Cricket Ground for the first time since 1985.
"Coming to Perth is probably the most extreme (conditions) we will face," New Zealand coach Gary Stead said.
"Perhaps if it was Melbourne or Sydney it would be a little more like home, so good on them for bringing us over here first.
"This is a different challenge than we have had for a while. We've had a lot of success at home and we play well there generally. But Australia also came and beat us there a few years ago."
On paper the New Zealand and Australia batting lineups look closely matched with Williamson for New Zealand and Steve Smith
for Australia occupying pivotal roles. For the first time six of New Zealand's top seven batsmen average better than 40 in tests while Australia has five batsmen averaging 40 or more.
Australia appears to have a substantial advantage in bowling. Cummins hasn't played a test against New Zealand but has 51 wickets in tests this year; Hazlewood has 32 wickets in tests against New Zealand at 32.63 and Starc 17 at 29.52.
New Zealand is sweating on the fitness of Trent Boult, who is recovering from a rib injury and who has 22 wickets in six Tests against Australia and 16 wickets in pink ball tests at 12.5.
Stead agreed the coming series against Australia and India will test whether New Zealand deserves its current ranking.
"I think after this summer you'll probably know a lot more," he said. "When you look at the program we have England, Australia and then India you'd argue they are up there with the best teams in the world. When we get to end of the summer I think it's probably an easier time for me to answer that.