An, who plays on the US PGA Tour, hit an eagle and five birdies in his five-under-par 67 to lead by a stroke from Australians Matt Jager and young amateur David Micheluzzi in tough, windy conditions.
Kuchar, who only arrived at Sydney’s The Lakes course on Wednesday morning after missing a connection in Los Angeles, is three off the pace, mixing four birdies with two bogeys.
The 40-year-old, who won his first tournament in four years at the Mayakoba Classic in Playa del Carmen on Sunday, is the highest-ranked player in the field at 29.
Another American who made the trip is Brandt Snedeker, a nine-time winner on the PGA Tour, but he struggled in the conditions to card 73 while Keegan Bradley, who won the BMW Championships this year, stroked a 72.
Defending champion Cameron Davis caved in under the home crowd pressure to card a 76 after a horrendous start when he put two shots in the water at the first then double-bogeyed the second.
An, ranked 51, benefited from going out early on a day when morning sun was quickly replaced by rain and wind whipping the course.
“It was weird. When I started, it was nice and sunny, it was a little breezy, but it wasn’t that bad, it was playable,” he said.
“Then got to the last hole and it came out of nowhere, it starts blowing a little harder and it started raining a little bit. So glad I finished before all that came.”
An, who was born in Korea but moved to the United States when he was 14 to attend the David Leadbetter Golf Academy in Florida, is gunning for his fourth international victory.
He won the Rolex Trophy in 2014 and the BMW PGA Championship and Shinhan Donghae Open in his home country a year later.
Kuchar admitted he struggled after the long trip Down Under and noted that the greens had “the most undulation I’ve ever seen”.
“And then with the wind blowing as strong as it was today, it was hard finding some fairways, it was hard trying to execute with good shots out there.” Snedeker is back at the tournament after more than a decade, having finished runner-up in 2007, but didn’t quite find his groove, with three consecutive bogeys hurting his chances.
“It was a little scrappy, I didn’t play great. I drove the ball pretty poorly. You do that around here, you’re going to struggle,” he said.