Eckstein has a long-standing date with United States Triple Crown winner Justify but is likely to be given the chance to further add to her record after victory in the Listed Winter Stakes.
Coolmore paid $750,000 for Eckstein at the recent National Broodmare Sale to become part of the team it is building to support the 2018 American champion who will stand in Australia in the spring.
The mare raced at the highest level when trained by Kurt Goldman and went within a short half head of a Group One victory in the 2017 Myer Classic when second to Shoals.
After her sale, she was transferred to the Chris Waller stable with last month's Tattersall's Tiara at Eagle Farm the target for a last-chance elite win.
She finished sixth but came through the race so well, Saturday's Listed Winter Stakes (1400m) at Rosehill came into focus.
Her class was to the fore, with Blake Shinn urging the $7 chance to the line a head in front of the favourite Gaulois ($5) with Nicci's Gold ($7.50) another short head third, thrilling her connections by getting black-type.
"Obviously she came to me in great order from Kurt Goldman," Waller said.
"I'm privileged to be able to take over the reins for the Coolmore team.
"It's a thrill and there is another race, the Winter Challenge, in a couple of weeks that we will look at."
In the past month, the champion trainer has been to Europe and Japan, visiting Coolmore's operation while he was in Ireland.
"It was a real highlight to meet the Coolmore team and to go to Ballydoyle and see how Aidan (O'Brien) operates," he said.
Eckstein was ridden by Blake Shinn who is scheduled to leave Sydney for Hong Kong later this month to take up a six-month contract.
Although Eckstein drew 13 of 14, Shinn said that was possibly to her advantage.
"She didn't have the best barrier or the best of runs but she actually seems to enjoy racing wide," Shinn said.
"It was just a matter of keeping her comfortable.
"She was dropping a lot in class today and her Group One ability shone through."