Webster spent his 31st birthday on Sunday preparing to join his first national squad, with Australia to converge on Adelaide on Monday ahead of the second Test that begins on Friday.
Even if the opportunity doesn't come in the day-night Test, he is in the box seat to debut at some stage this summer as selectors stew on Mitch Marsh's bowling workload and fitness.
Webster's journey to a possible debut is one of the more unique of any player this century.
Since 2000, only Bryce McGain has debuted for Australia at an older age in Test cricket without having played some form of international cricket in their twenties.
One of the more experienced players in the Sheffield Shield, Webster debuted for Tasmania in February 2014.
The allrounder only rose to prominence in recent years, after averaging 29.54 with the bat in his first eight years of first-class cricket.
But since hitting a breakthrough 166no against Queensland in March 2022, Webster has scored 2402 runs at an average of 57.1.
"I'm hugely proud of it," Webster told AAP.
"The early days of my career, the biggest knock was I was always inconsistent. I was shuffled around the order from opening down to No.6.
"I would get one hundred a year and a run of low scores.
"To be able to continually have some success now over three summers is really pleasing. It is something I have worked hard at and tried to maintain my routines.
"So it is very pleasing to see some results now."
Beau Webster has proven handy with bat and ball in recent seasons. (Dave Hunt/AAP PHOTOS)
Webster's rise has coincided with him becoming a medium-pace-bowling allrounder in recent years, while still having the ability to take wickets with offspin.
That three-pronged nature of Webster's game could make the 200cm-tall Tasmanian an asset on Australia's tour of Sri Lanka later this summer, where he could fill multiple roles in the same team.
Those close to Webster also believe the Tasmanian's rise comes from better knowing his own game.
He bounced around positions in the batting order early in his career, and has scored centuries as an opener, No.3, No.5, No.6 and No.7 against the pink and red ball.
But he has made his name by starring at No.6 for Tasmania in recent years, topping the Shield's run-scoring charts last summer and being named player of the tournament.
"Through all those years and opportunities he has played, he's learned a lot about himself and his own game," Tasmania coach Jeff Vaughan said.
"He's learned a lot about who he wants to be, and he's really trusting now in the cricketer he wants to be and the cricketer he is.
"It's come from a lot of hard work, a lot of games, opportunities and ups and downs over a 10-year period.
"I've got no doubt he can be successful. This isn't a question of him trying to find his way in first-class cricket, he is genuinely dominating it.
"And history suggests that the players who stand out at our level often go on and have success at the highest level."