The probability to break a long drought in Australia is highly unlikely given that the Sri Lanka side folded inside two and half days in the second Test despite Australia experimenting with player rotation in every game.
Sri Lanka have not won in 12 games in Australia since 1988 and the hosts' mammoth innings and 201-run victory wrapped up the three-Test series with only pride to play for in Sydney.
Their next assignment in the continent is four years away, making the gap longer if they do not win this week.
"It was really hard to digest that defeat [in two-and-a-half days at the MCG], but that's in the past now," the batsman Thilan Samaraweera said.
"The good thing is this team have the belief they can make history by winning one Test in Australia.
"That is the kind of attitude we have going into the New Year's Test.
"We have nothing to lose. We're 2-0 down, but these 16 players and 10 in the management team want to go out by winning this Test."
The injury-hit visitors' woes were mounting as they will be without the veteran Kumar Sangakkara (finger) and the paceman Chanaka Welagedera (hamstring) for the clash, while two other players are doubts.
The wicketkeeper Prasanna Jayawardene (thumb) and the fast bowler Nuwan Kulasekara (rib) will need to pass fitness tests tomorrow, with Samaraweera labelling the pair "50-50" to play.
The young batsman Lahiru Thirimanne was set to join the squad on Monday, with the fast bowler Suranga Lakmal to follow on Tuesday after visa issues delayed his arrival.
Lakmal, 25, has been sidelined with injury since April but boasts a decent record against Australia, having claimed a career-best three for 55 in Galle last year.
The match will also be Mahela Jayawardene's last as the Sri Lanka captain before Angelo Mathews takes over.
"This is the right time for Mahela to step down," Samaraweera said. "We have to move on for the future."
"It gives Angelo a chance to captain while three or four senior players are still playing and will help with the pressure."
Australia, on the other hand, are set to play a fourth debutant this summer.
With Phil Hughes already recalled to replace Ricky Ponting, Usman Khawaja will get first crack at the retiring Michael Hussey's spot. The uncapped all-rounder Glenn Maxwell is also in the 13-man squad as the replacement for the injured Shane Watson.
Maxwell can be a handy bat at No 7, bowls off-spin and is a reputed fielder. Jackson Bird, who kicked off his career in the second Test at Melbourne, did well but will make way for the in-form Mitchell Starc, the fast bowler he replaced.
The Sydney Cricket Ground will witness lot of pink colour in support of a cancer charity, the McGrath Foundation founded by Jane McGrath and her husband Glenn McGrath.
The former fast bowler will be inducted as the 68th member of the Hall of Fame by the International Cricket Council at the venue after the first session in the morning tomorrow.
Organisers are also requesting the fans to wear wide-brimmed hats and nose sunscreen, as tributes to the departed Tony Greig and the retiring Hussey, respectively. A moment's silence will be observed and black armbands will be worn to as a show of respect to Greig, 66, who died of cardiac arrest while fighting lung cancer.
"He was a great human being and a great voice for Sri Lanka," Samaraweera said of Greig.
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