Sam Konstas, back in the opening hot-seat, and an uncomfortable-looking Cameron Green were both sent packing for three apiece by the Aussies' excellent old tormentor Shamar Joseph after Cummins had won the toss and decided to bat at the Kensington Oval.
Then without either the old steadying influence of the injured Steve Smith and dropped Marnus Labuschagne to call on, the newly installed No.4 Josh Inglis got out trying rashly to counter-attack Jayden Seales, hoisting an attempted pull high off a top edge and getting caught behind by Shai Hope for five.
That left the visitors reeling at 3-22 after 15.1 testing overs - and it could have been worse if the West Indians had taken two earlier chances to get rid of a scoreless Green, third ball, and Usman Khawaja, who was dropped at first slip, also off Joseph, for six.
Khawaja (32no, including a hoiked six over midwicket), in particular, felt like a costly drop for the home side as he began the recovery job with Travis Head (21no including four boundaries), the experienced pair taking Australia to lunch with an unbroken 43 partnership.
As is traditional at the famous venue, staging its first Test since 2022, the visitors were keen to cash in first-up at the Kensington Oval on Wednesday as they dropped Labuschagne for the first time in six years following the loss in the World Test Championship final against South Africa two weeks ago at Lord's.
Smith was also out of action because of the finger injury he suffered in the final, although he could be available for the second Test.
It was a big opportunity again for Konstas, who made a spectacular debut in December against India at just 19, but he was quickly dismissed by Joseph nipping one back that trapped him lbw on review. He lasted 14 balls for his three.
Green looked as unhappy as he had against Kagiso Rabada at Lord's before finally being put out his misery when Joseph got him caught pushing hard to second slip Justin Greaves on the 21st ball he faced.