White, who has played 37 Tests since making his debut in 2013, missed the three-Test series win over France because of a knee injury, but watching on, he felt the new Wallabies got some invaluable experience in high-pressure situations.
"That French team is a bloody good team, and that last game especially, going a man down, it's a lot of pressure there to win a series on home soil," he told rugby.com.au.
"Guys showed a lot of ticker there, and I think it's only going to hold us in good stead. Sometimes we get the All Blacks first game of the Test season, it was good to have someone else to warm into these games."
White said he had been doing well in his recovery and was told by team medicos that he should be good to be in the hunt for a place in Auckland's Test.
"It's coming along really well. [I'm] just taking it day-by-day, which is really [a] cliché, but it's feeling good.
"I'm back training now, so fingers crossed I'm able to contribute in some capacity over the next couple of weeks."
He said he hoped to be available for Saturday.
White said the team would be in a good place to give New Zealand a good shake.
"We're going to the cauldron of Eden Park, and it's going to be a step-up again. It's coming off some good experience there, and it feels like this time is a little bit different," he said as they look to end a run of losses that has extended since 1986 at the ground.