Will Pucovski was dropped twice on his way to a half-century on debut as Australia recovered from an early setback to build a promising first innings in the rain-hit third Test against India Thursday.

After David Warner's early departure for five, wicketkeeper Rishabh Pant twice dropped Pucovski who shared an 87-run partnership with Marnus Labuschagne.

Batting after captain Tim Paine won the toss, Australia were 93 for one at tea after more than three hours' play was lost due to persistent drizzle at the Sydney Cricket Ground.

Only 35 minutes of cricket was possible in the first session, but it was enough for Mohammed Siraj to grab the key wicket of Warner on his return from injury, caught by Cheteshwar Pujara.

Pucovski resumed on 14 and Labuschagne on two in front of some 10,000 socially-distanced fans, a quarter of capacity, when play finally resumed at 3pm.

By tea, Pucovski had moved to 54 and Labuschagne 34 in a Test both sides are desperate to win with the four-match series level at 1-1.

But the 22-year-old debutant was fortunate to still be at the crease.

He had a big let-off on 26 when Ravi Ashwin enticed a thin edge, but Pant failed to take what should have been a simple catch.

Three overs later and Pant did it again. 

Pucovski, on 32, got a glove to a rising Siraj ball and as Pant dived, the ball popped out of his hand. He made another grab and seemed to have caught it, but replays showed the ball hit the ground first.

Pucovski then survived a run-out opportunity after a misunderstanding with Labuschagne, but refocused to bring up his 50 with a boundary off fellow debutant Navdeep Saini. 

Australia have high hopes for Pucovski, who scored two double centuries in the Sheffield Shield this season but had been sidelined with a concussion, the ninth of his short career.

India tried to unsettle him early with Jasprit Bumrah sending down a bouncer on his fifth ball, but Pucovski was unfazed and soon got off the mark, hitting his first Test four off a Siraj short ball as he gained in confidence.

The stoic Labuschagne has been Australia's best batsman this series and played some authoritative strokes, but he too was lucky to survive an edge off Bumrah on 11 which just failed to carry to slip.

Veteran Warner missed the first two Tests in Adelaide and Melbourne with a groin injury and his return was highly anticipated. But he didn't last long.

He showed intent with a two off his first ball but his natural aggression brought him undone, swinging at a full Siraj delivery which took at outside edge and flew to Pujara at slip.