Australia are not yet a great team but completing a series sweep in Sri Lanka would push them closer, according to spin bowler Nathan Lyon.
Australia won the first test by an innings and 242 runs in Galle and will look to wrap up the series 2-0 with another win at the same venue when the second test starts on Thursday.
The world's top-ranked test nation and reigning World Test Championship holders, Australia have won 10 out of their last 13 tests since drawing the 2023 Ashes in England.
On their last tour of Sri Lanka, Australia gave up a 1-0 lead to split the two-match series with the hosts, who rebounded with an innings and 39-run win in the second test in Galle.
Lyon said there was plenty of motivation in the Australian camp to avoid a repeat of that let-down.
"It's about us on our journey to becoming a great team, to make sure we go 2-0 up," he told reporters.
"We're on that journey, we're not there yet but that's our end goal.
"We want to be known as a great team, and part of that journey is when we close a window making sure we nail it shut, and we don’t let anyone back in."
Australia's success has been compared with some of the nation's great test teams led by Steve Waugh and Ricky Ponting.
Asked what would elevate the current group into greatness, Lyon said Australia still needed series wins in India and England.
Australia were held to 2-2 draws on their last two Ashes tours of England and have not beaten India away since Adam Gilchrist's team took a 2-1 series win in 2004.
Australia are likely to retain the same three-prong spin attack of Lyon, Matthew Kuhnemann and Todd Murphy for the second test after they took a total of 17 wickets in the first.
"I think we all complement each other really well, with three totally different bowlers with three totally different mindsets as well," said 37-year-old Lyon, who took seven wickets in the series-opener.
"I feel like I'm learning off Todd and Matt, and I feel like they're pushing me to try and get better as well.
"Hopefully I'm passing on a bit of knowledge here and there."