A nine-month-old girl whose body washed up on Surfers Paradise beach was likely still alive when tossed into a river by her mentally ill father, a judge has heard.
The 49-year-old man later claimed to have "sacrificed" the infant as her upcoming first birthday "would have meant the end of the world", his NSW Supreme Court trial was told on Monday.
The homeless man allegedly carried his daughter through torrential rain and "cast her" into the Tweed River as his partner and young son sheltered in the Tweed Mall car park on November 17, 2018.
"It is possible (she) had already been smothered. However, it is more likely she was still alive and drowned," crown prosecutor Brendan Campbell said in his opening address.
Currents and tides took the girl 20 kilometres north to the famed Gold Coast beach, where an 18-year-old school leaver made the grim discovery while on a midnight walk on November 19.
While in police custody and appearing "floridly psychotic", the man was recorded saying he'd sacrificed the girl to save all the children of the world.
"(He said) if she'd turned one it would have meant the end of the world," Mr Campbell said.
"There were garbled biblical themes accompanied by grandiose statements."
He also told police the girl was a "corruption" and a "demon", contending it was his "prophecy" to kill her.
The accused man cannot be named, as doing so would identify his son.
A forensic psychiatrist is expected to tell Justice Helen Wilson that the father had a long history of delusional beliefs involving infants and suffered from a schizophrenic disorder.
At the time of the girl's death, her father was labouring under a defect of reason from a disease of the mind and therefore was unaware his act was morally wrong, Professor David Greenberg is expected to say.
Justice Wilson, who is hearing the trial without a jury, is expected to hear the relationship between the accused man and the girl's mother was marked by mental illness and domestic violence.
The woman fell pregnant with the couple's son soon after they met in March 2016.
Her second pregnancy in 2017 made the father unhappy and he tried to have relatives take the baby before and after the girl's birth in February 2018.
The young family of four lived an erratic lifestyle, living at times in a tent at Broadbeach, in a motel room at Surfers Paradise and out of a van at Chris Cunningham Park on the banks of the Tweed.
Amid continuing episodes of domestic violence, the children's mother determined to leave her partner and return to her family in Geelong in October 2018.
Flights were booked but she and the children never boarded the plane after she apparently decided against keeping her son from his father, Mr Campbell said.
The father then became increasingly violent towards the mother and disdainful to his daughter.
The morning of his daughter's homicide, he convinced his partner to hand over the infant to a homeless woman.
That woman soon realised she was unable to care for the baby, and returned her before a large storm swept over Tweed Heads, Mr Campbell said.
The trial continues.
1800 RESPECT (1800 737 732)
Lifeline 13 11 14
beyondblue 1300 22 4636