Kim fired eight birdies and just one bogey on Thursday in the tour's return to Utah for the first time in 60 years to be tied for fourth.
South Korea's Haeran Ryu leads the way after a nine under 63 for a one-shot lead over Thailand's Ariya Jutanugarm and Wei-Ling Hsu from Chinese Taipei.
Kim looked set to make a charge at the leaders, with consecutive birdies on the run home, but a bogey with three holes to play stalled her run.
She recovered to finish birdie, par, par to head into the second round full of confidence.
Fellow Australians Karis Davidson and MinJee Lee were solid in the opening round, both firing two under 70s for a share of 42nd place.
Both went bogey free across the 18 holes but could manage just the two birdies.
Ryu missed only one fairway, one green and took 27 putts in her round after sharing the 54-hole lead last week in the Chevron Championship.
Nothing went right for her the final round in Texas. Even with an eagle on the final hole, she shot 76 and missed the playoff by two shots.
"I'm not change something from my mind, because last week it was a tough golf course and this week it's tough, too," Ryu said.
"Just thinking more accuracy for my shot, and I think same as last week."
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