Warner is 15 not out, having already driven three boundaries, while Marcus Harris is unbeaten on 11 after 12.3 overs.
The start of play at the SCG was pushed back to 11am AEDT because of showers, while more rain stopped play twice in the morning session.
Further rain is expected on Wednesday and throughout the match.
Warner and Harris negotiated Jimmy Anderson and Stuart Broad's opening spell with few nervous moments.
Express paceman Mark Wood was halfway through his first over when umpires called for the covers at 12.33pm AEDT.
Pat Cummins opted to bat under overcast skies, backing Warner and Harris to excel on a green-tinged pitch.
"It looks a really good batting wicket," Cummins said after winning the toss.
"Probably more grass than we normally expect here.
"Openers have to work hard this morning, but runs are there.
"SCG has always been a bat-first wicket."
England captain Joe Root said he would also have batted first if given the chance.
Australia and England named their respective line-ups on match eve, both opting for one change.
Usman Khawaja is playing his first Test since 2019, having been called up in the absence of Travis Head to bat at No.5.
Head remained in Melbourne, having contracted COVID-19 after the Boxing Day Test.
The tourists recalled veteran paceman Broad in place of Ollie Robinson.
Australia hold an unassailable 3-0 lead in the five-Test series, having crushed England by an innings and 14 runs at the MCG.
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