The top-ranked Australian at world No.5, Green arrived in Houston having banked her fourth win of the year with victory in the prestigious LA Championship.
But Green's hopes of securing her second major championship title took a blow with the Perth product tied for 59th on a crowded leaderboard at one over, after a costly double bogey on the par-four 12th.
Sydney's Cassie Porter is the best of the eight-strong Australian contingent with a round of two-under 70 to sit tied 18th.
Struggling with illness, West Australian Minjee Lee, who is trying to win her fourth of the LPGA's five majors, was two over in a tie for 80th.
Starting on the 10th, Korda pocketed two birdies before heating up to sink three straight between the first and third.
The American world No.2 then added a pair on the seventh and eighth to finish her round at seven-under-par 65 - her best start to a major in four years.
The soggy Memorial Park Golf Course has endured significant rainfall this week. Korda got in some extra work in the rain earlier in the week and felt that contributed to her impressive start.
"Tuesday I came out and putted in the rain when we were allowed to before the pro-am and also Wednesday," Korda said.
"It feels good to put a good round together ... just day one out of four - a lot can happen.
"So happy to be in this position and hoping to move forward."
In four LPGA starts this season, Korda has won the season-opening Hilton Grand Vacations Tournament of Champions and followed that with three straight second-place finishes.
Thailand's Patty Tavatanakit and South Korea's Somi Lee are tied for second at five under.
Tavatanakit began her day with two birdies among her first three holes and never wavered in a bogey-free performance.
Lee, a winner at the 2025 Dow Championship, carded six birdies and was in line for an even better finish before she suffered a bogey on her final hole of the day, the ninth.
Defending champion Mao Saigo of Japan struggled to a one-over 73 while world No.1 Jeeno Thitikul had four bogeys over her last eight holes and shot 74.
with Reuters
