Cummins was ruled out of the series-opener in Perth starting on November 21 but hopes to be available for the following match in Brisbane two weeks later.
The 32-year-old paceman bowled off a short run-up in the nets at Cricket New South Wales' training base on Tuesday as staff watched on.
Australia head coach Andrew McDonald said on Monday Cummins would need "four-plus weeks" to be ready to play, effectively ruling him out of any warmup match before the Gabba test.
Steve Smith will captain Australia in Perth, while Victoria fast bowler Scott Boland is expected to be selected in Cummins's place.
Australia hold the urn, having retained it with a 2-2 series draw in the 2023 Ashes in England.