On Thursday, New Zealand won a crucial toss and cashed in on perfect batting conditions, with England forced to work with the ball in the extreme heat.
But after captain Latham was out for 151 and Conway fell for 157, Rachin Ravindra and Henry Nicholls were dismissed by the final two deliveries of the day to raise England's hopes.
And, under Stokes, England have form for winning despite conceding a huge first-innings total.
In Test history, 18 teams have been beaten after posting 500 in their first innings. The last three defeats have been inflicted by England – New Zealand here, then Pakistan in Rawalpindi in 2022, and Pakistan again in Multan in 2024.
"The wicket is pretty good, so I would imagine the first two innings are going to be good for batting, then we'll see what happens later in the Test," said Southee.
"Test cricket is played over five days. You saw here in the Test in 2022 both first-innings scores were very high.
"Throughout the whole Test you've got to believe you're still in a position where all results are possible. We sit here on day one with New Zealand four down, two new batters tomorrow, nightwatchman at one end and the new ball in hand. It's an exciting time to go into day two."
England are desperate for a series win after months of poor results and off-field issues. They have won only two of their past nine Tests and this series has been dogged by a nightclub controversy involving captain Ben Stokes and pace bowler Gus Atkinson.
Prior to this match, Stokes said the pressure on his team is the highest it has been in his four years in charge.
New Zealand, meanwhile, have the opportunity to become the first visiting team to win a series of three matches or more in this country since 2012.
And their assistant coach Luke Ronchi countered Southee's suggestion that the defeat of 2022 will be a factor in the remainder of this match.
"It's a very different team compared to 2022," said Ronchi, who played international cricket for New Zealand and Australia.
"It's different cricket. It's a different surface. That hasn't really come into it. It's four years ago.
"The boys are being in the moment, understanding what is needed each ball and how they want to go about it. That's all we can ask of each other."
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