A baby girl was most probably born alive before she was later found in a shallow sand grave at a southern Sydney beach, an inquest has found.
The finding came as the coroner recommended the state government consider the installation of baby boxes or hatches at hospitals where distressed mothers could leave their babies.
On a Sunday morning in November 2014, a baby since named Lily Grace was found at the southern end of Maroubra Beach by nippers digging holes in the sand after a flag race.
The inquest at the State Coroner's Court on Wednesday heard the three boys were playing in the dunes when they started shouting, "Dead baby! Dead baby!"
Police recovered the decomposed body of Lily Grace, who a pathologist believes was aged between 38 and 40 weeks when she died.
There were no physical or internal signs of injury and, despite an exhaustive police investigation, it is not known how she died.
The inquest also heard it was impossible to tell for how long Lily Grace had been left in the sand, what her ethnicity was and who her mother was.
"This is a very sad case and, quite obviously, one of the saddest aspects is that we don't know who Lily Grace is," Deputy State Coroner Hugh Dillon said.
"Although we do not know who [the mother] is, it takes little imagination to understand that to lose a baby and to seek to hide that baby's death in this way suggests that the mother was desperate," he said.
"The fact that she has not come forward suggests that she is ashamed, vulnerable and scared."
The inquest focused heavily on whether Lily Grace had ever lived.
Pathologist Isabel Brouwer told the court that Lily Grace had weighed 2.23 kilograms at birth. Statistically, fewer than 1 per cent of babies born between the weight of 1.5 and 2.5 kilograms could be stillborn.
Dr Brouwer also said it was unlikely the baby was born in a hospital, because of the way the umbilical cord had been cut.
"Commonsense suggests that it is more probable than not that she was born alive," Mr Dillon said.
The police investigation, headed by Detective Senior Constable Erin Cordina, was extensive.
Officers met 57 women who gave birth at hospitals in south-eastern Sydney and physically saw their babies.
The inquest heard how Maroubra woman Filomena D'Alessandro and her husband Bill Green had become the unofficial parents of Lily Grace and named her so she could be laid to rest with dignity.
Ms D'Alessandro, a mother-of-three, worked with authorities to give Lily Grace a proper funeral on April 29 last year.
That day has since been named Lily Grace Awareness Day, and will be a day to remember all unidentified children who have died.
In closing, Mr Dillon said he supported "safe haven laws" and recommended the state government consider the installation of "baby boxes" for mothers to leave thier babies, as was done in Germany, Canada and the Czech Republic.
"Safe haven laws allow parents to hand over their babies without risk of prosecution by authorities.
"They enable desperate [mothers] to come forward without fear of humiliation and prosecution to hand over their babies to someone who will safeguard them," he said.
Outside the court Ms D'Alessandro said she wished to help the mother who abandoned Lily Grace.
"If we could do anything to help you, no one is out to get you, it's beyond that now.
"You need the help and there are people out there who are going to help," she said.