The Football Ferns had never won a game in 15 attempts at the finals before defeating former champions Norway 1-0 in Auckland on Thursday in the opening match of the tournament.
Now they face the Philippines on Tuesday knowing that another victory could secure their place in the last 16 even before their final Group A match against Switzerland.
"I'd like to think we don't have a ceiling," said Bott, the Leicester City defender, when asked how far New Zealand could go.
"You should never set yourself limits. The Norway game has set a new standard for us and we don't go down from there."
After that opening result anything less than a win against debutants the Philippines in Wellington would be considered a disappointment.
New Zealand is not traditionally a football nation but the team's historic success, thanks to Hannah Wilkinson's goal, has thrust them into the spotlight like never before.
The victory over Norway was watched at Eden Park by over 42,000 fans, a national record crowd for football in the country, men's or women's.
"I think we still in a sense have the weight of the country on our shoulders," added the 28-year-old Bott.
"There is always a certain amount of pressure but it has given us the boost we need and we have taken a lot of confidence from it."
The New Zealand team faced disruption late Saturday when they were forced to evacuate their hotel in central Auckland because of a fire.
Local media reported a man had been arrested and charged with burglary and arson after the incident, which came less than 72 hours after a deadly shooting in Auckland on the morning of the opening match.
The team was not thought to have been the target of the hotel fire and nobody was hurt.
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"We went down the fire exits. One was a bit smoky but the majority of us got down the other exit," said Bott.
"We spent the rest of the evening in another location until the hotel was clean and everything was safe to go back.
"As a team, we have no cause for concern. Things are back to normal for us."
As European champions and one of the favorites to lift the Women’s World Cup, England was always expected to make a winning start.
At least the Lionesses can tick that item off the checklist.
Beyond that, there were few positives to take from an unconvincing 1-0 victory Saturday night against Haiti, which was making its debut at the global tournament.
A twice-taken Georgia Stanway penalty was the difference between the teams that are ranked fourth and 53rd by soccer’s world governing body.
“It’s so important to win your first game in a tournament. It’s been a long build-up to today and we’re kind of happy to just get over the line,” a relieved Stanway said in the wake of the game.
The sense back in England was that it was an underwhelming start for a team that has had its problems recently.
Haiti — particularly through the outstanding 19-year-old forward Melchie Dumornay — could yet throw up some surprises at the tournament being co-hosted by Australia and New Zealand.
England’s struggles in Brisbane, however, seemed to be more of its own making as its run of game time without a goal from open play stretched to more than seven hours, including a behind-closed-doors warm-up game against Canada that ended 0-0.
Injuries have undoubtedly disrupted England’s preparations with key players Beth Mead, Fran Kirby, and Leah Wiliamson all ruled out. Captain Millie Bright started against Haiti in a return from a knee injury she sustained in March, and she appeared to be uneasy for much of the game.
A dispute with the English Football Association over bonuses and commercial arrangements has also cast a shadow over the build-up, even if the players have decided to pause negotiations to focus on the World Cup.
Coach Sarina Wiegman needs to find a way to get her team back into gear on the field after the triumph of last year’s Euros.
Only six members of the lineup that started the final against Germany at Wembley last July were in the XI on Saturday, and consequently, England lacked cohesion.
Most notable was its lack of cutting edge.
Record goalscorer Ellen White retired and is working as a pundit for the BBC during the tournament.
In her place against Haiti was Alessia Russo, who was the subject of a reported world record bid worth 500,000 pounds ($642,000) from Arsenal last season as a result of her outstanding form for Manchester United. She eventually joined the London team as a free agent this month and was selected for England’s World Cup opener ahead of Rachel Daley, the leading scorer in the Women’s Super League.
Despite that show of faith from Wiegman, Russo wasn’t able to get her World Cup account up and running. England’s attacking threat was hardly improved when Daley replaced her in the 76th minute.
It wasn’t that England didn’t have its chances, registering 19 shots with 10 on target. It was an issue of its failure to convert.
“We did create chances, but we lost the ball and then they were gone. That was hard for us,” Wiegman said. “Sometimes we had the last pass instead of shooting ourselves. I hope the next game in open play we can score a goal.”
Wiegman had wrestled over the decision about who to start at the point of her attack, and that may be her biggest dilemma again ahead of England’s second Group D game against Denmark in Sydney on Friday.
The Netherlands kicked off their Group E campaign with a 1-0 win over Women's World Cup debutants Portugal at Dunedin Stadium on Sunday thanks to a first-half goal from Stefanie Van der Gragt that was awarded on a VAR review.
The Dutch edged Portugal 3-2 a year ago in the European Championship group stage, but this time the Iberian side was no match for the team in their trademark orange and did not have a shot on target until the 82nd minute.
The Dutch scored in the 13th minute from a corner kick when Van der Gragt rose above the defense at the far post to head home, but the flag went up for offside when the lineswoman deemed Jill Roord to be obstructing the goalkeeper.
However, the offside decision for interfering with play was overturned on a VAR review by the referee after she watched a replay on the monitor and the goal stood, sparking a second celebration from the Dutch team.
Roord nearly made it 2-0 minutes later when she had a free header in the six-yard box, but the unmarked midfielder headed over the bar to hand Portugal a lifeline.
Portugal, however, failed to muster a shot on goal in the first half while at the other end, they thwarted waves of attacks from the Dutch.
The story was the same in the second half when Portuguese keeper Ines Pereira denied Danielle van De Donk with a fine reflex save after some clever passing to set up the midfielder.
Portugal substitute Telma Encarnacao finally created their best opportunity in the 82nd minute when she charged down the right flank and cut in to shoot, but Dutch keeper Daphne van Domselaar was up to the task and parried her attempt.
The Netherlands move level with group leaders United States on three points but sit second on goal difference ahead of Thursday's titanic clash - a repeat of the 2019 final where the Americans won their fourth World Cup crown.