Australia bowlers Starc, Josh Hazlewood, Pat Cummins were handed first use of the Brisbane pitch after Joe Root won the toss and elected to bat first.
Root said he wanted his side to ‘bat big’ at the toss but England’s first innings got off to a terrible start as Cook was dismissed in the third over of the match.
Playing tentatively forward to a full ball, Cook could only get a feather on Starc’s delivery and Peter Handscomb made no mistake at first slip.
BT Sport pundit Graeme Swann said: ‘Cooky’s right back on his stumps, he should have been trying to get down the pitch more. It’s obviously a bad start for him and England.’
Former Australia wicketkeeper batsman Adam Gilchrist added: ‘He was just reaching, there’s a lack of pace in this pitch and that lured him down and he was reaching for the ball.’
Speaking before the opening day’s play in Brisbane, Swann branded Steve Smith’s Australia as ‘overrated’ and backed England to defy the odds by defending the Ashes.
‘No one is giving England much of a shout so far but I’m going too,’ the ex-spinner said.
‘I think England will win this series 2-1 and win this Test match here in Brisbane. Australia are overrated in my opinion and I can’t wait to be proven absolutely right.’