The Australian duo are three behind first-round leader David Lipsky, who birdied four of his final six holes at the Silverado Resort's North Course, en route to a five-under 32 on his back nine.
Lipsky leads Scot Martin Laird and Patton Kizzire by one, while tied for third at five-under are Mark Hubbard, Kevin Dougherty, Wilson Furr, Kevin Streelman and Joel Dahmen.
The Procore Championship is the first of eight events on the PGA Tour's "FedEx Cup Fall" schedule, which will help determine players' eligibility for the 2025 season.
Players need to finish the autumn in the top 125 in the standings in order to keep their Tour card. Finishing between Nos.126-150 will give players conditional status next year.
Lee and Baddeley are joint ninth in the tournament. Baddeley had six birdies mixed with two bogeys, while West Australian Lee had five birdies with his only blemish on the par-four sixth.
Baddeley is currently No.152 in the standings and is fighting for his card while Lee sits comfortably in 60th position.
One shot behind them is compatriot Jeffrey Guan, who is in a tie for 22nd.
Lipsky needs all the help he can get, as he started the week No.163 on the list.
After most of his birdie putts came from inside 10 feet, he drained a 12-footer at the par-5 18th to move to seven under.
Hubbard has had a memorable week so far, not necessarily for the right reasons. He was fully qualified for the Procore Championship but forgot to register in time, then decided to attempt to play his way into the field via Monday qualifying.
He posted the best round of the day Monday to push his way into the field. Come Thursday, he racked up nine birdies with one bogey - and a triple bogey at the par-3 17th hole, where his tee shot found the water and he used five strokes just to get on the green.
"Golf is impossible," Hubbard said, according to PGATour.com. "I'm just doing a little bit better job of accepting things and I think that carried over on Monday and then also carried over into my back nine today after that triple."
Among notable names, defending champion Sahith Theegala and Tom Hoge opened with three-under 69, while Wyndham Clark posted a 70 and Max Homa a 71.
Those four players are already secure for next season after finishing in the FedEx Cup top 50.
Theegala and Homa are California natives who have combined to win the past three tournaments in Napa.
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