The 74-year-old is accused of engaging in sexual activity with a girl known during the trial only as AB, between July and December 1980, while she was aged 16 and his student.
Dawson denies the charge, pleading not guilty on Tuesday in the NSW District Court.
Crown prosecutor Emma Blizard said it is not in dispute that sexual activity took place between the two, who later married.
"The central issue will be one of timing and when events commenced," Ms Blizard said.
Dawson first noticed the girl in 1979 and then "made his own arrangements for her to be in his class the following year," she said.
He paid particular attention to her and she began confiding difficulties she was having at home, before he allegedly put his hand on her knee at a sports carnival, Ms Blizard said, describing the expected evidence of a witness to the first instance of any physical contact between the pair.
AB later started babysitting Dawson's children and the pair kissed in his car, a few days or weeks before alleged sexual activity took place when he drove her to his parents' home in Sydney's south at Maroubra, Ms Blizard said.
Public defender Claire Wasley reminded Judge Sarah Huggett she is not required to judge Dawson by contemporary legal or moral standards, and what she knows about his conviction for murder should have no bearing on the trial.
Sexual activity commenced between between Dawson and AB while she was under 18 and a student at Cromer, but not one of Dawson's, Ms Wasley said.
AB is due to give evidence as the trial continues on Tuesday.
Dawson was jailed in 2022 for murdering his wife Lynette in January 1982, with a judge finding he was motivated by a desire to pursue an unfettered relationship with the student.
Health issues in his old age mean Dawson will be given more frequent breaks during the judge-alone trial.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
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