The man, whose identity is suppressed, has been charged with child homicide and is facing trial in the Supreme Court.
Prosecutors have alleged he violently assaulted the baby in a moment of intolerance and frustration - shaking him, striking him, or both after he awoke crying and screaming about midnight.
He initially told paramedics the 24-day-old just went limp in his arms after his partner went to fetch a bottle of milk, the jury was told on Tuesday.
Rishi Nathwani SC said his client confessed to a doctor that he dropped his son. (Aap/AAP PHOTOS)
His lawyer said the father repeated the claim at hospital, where the baby later died in November 2017, however police looked into the case and uncovered a different story.
Officers found out the man went to a doctor about his depression and confessed he actually dropped his son, defence barrister Rishi Nathwani SC told the jury on Wednesday.
"It is accepted by (my client) that he was not telling the whole truth," Mr Nathwani said.
"(But) are there reasons to say (the baby) went limp that are consistent with innocence?"
The man denied the charge of child homicide, he said.
He flagged the defence would question whether a forensic paediatric practitioner, who looked at the baby's injuries, came into the case with a closed mind.
What was in dispute was whether she "went from an impartial expert to an investigator or an advocate," Mr Nathwani said.
The fairness and impartiality of the police investigation would also be questioned, the barrister said.
"There's no dispute there are a number of injuries but there is a dispute about what they mean," Mr Nathwani said.
The accused father had no criminal convictions and had worked as a chef, he said.
Prosecutor Mark Gibson KC on Tuesday told the jury the baby died in hospital after sustaining catastrophic injuries, with bruises to his scalp, blood on the brain, brain swelling and bleeding to his eyes.
The injuries raised concern they were non-accidental, and their extent was revealed in scans, he said.
"This case is about what happened in those few minutes in the master bedroom," Mr Gibson said.
The trial continues.
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