Buhai carded a bogey-free 63, while Liu holed a short eagle putt on the par-5 16th hole to join the South African atop the first-round leaderboard.
Green has won the past two editions of the event, collecting $US562,500 ($A880,000) for her win at Wilshire Golf Club in 2024.
But, with this year's tournament shifting to the El Caballero Country Club, Green struggled early.
The two-time defending champion, who started on the back nine, crashed to two over after bogeying her third and fifth holes.
The Australian immediately recovered with four straight birdies, ultimately finishing tied 44th at three-under 69.
"I was back in Australia the last two weeks, so I think I'm mentally in a very good state," Green said prior to the tournament.
"It's a good course ... there's going to be some tough holes, easier holes. It's a nice combination.
"I've had a lot of volunteers and other people in the crowd say they're hoping for me to do a three-peat, obviously I'd love to have my name in history, but I don't want to put too much pressure on myself."Â
Green is raising money at the tournament to help fund fire-recovery efforts in Los Angeles, donating $US500 for each birdie and $US1,000 for every eagle.
"There's people who aren't going to be in their own house for years. So even though the fires have stopped, there's still a lot of pain that people are suffering," she said.
"Hopefully it brings some awareness ... California has been such a special place to my heart."
Sweden's Frida Kinhult birdied the last three holes to claim third place at 64.
Minjee Lee Lee was the best of the Australians on day one of the event, ensuring she remained in the mix with six birdies.
Lee is tied 15th at five-under 67, while compatriots Green, Steph Kyriacou and Cassie Porter are a further two strokes behind but above the projected cut line.
