The baby girl, whose remains were found in a shoebox in Sydney almost two years ago, was buried Thursday morning in a rose-covered coffin. She was called "Bridget," after the Irish saint Bridget of Kildare, the patron saint of babies.

Police still calls on Baby Bridget's mother to show up, saying authorities are not after making an arrest, but providing "closure."

Baby Bridget was found by a gardener on Beresford Road, Strathfield on August 19, 2010. Police had hoped that the baby's mother would come forward during the course of investigation.

Nine reported Baby Bridget was found wrapped in a towel inside a black cardboard box. Her umbilical cord had not been cleaned up, AAP noted.

"In many ways it is curious to be saying goodbye to a little girl who was a beautiful stranger," Reverend Ken Fischer said during the funeral service.

"For baby Bridget life is no less significant and in fact the care and the love that has been showed to her by people that didn't know her is touching and inspiring," the reverend said.

Detective Sergeant Dennis Knezevic told the AAP authorities wanted to find Baby Bridget's mother, because she may be needing assistance.

"(Baby Bridget's interment) is just one part of it and the coroner's inquest will be the finale in the investigation," he said, noting the mother has until then to come forward and identify herself before the authorities.

"We hope that the mother, or anyone who might have links to baby Bridget, will come forward and tell us how baby Bridget came to be in those gardens, and (because) possibly the family and her mother may need assistance," said Detective Knezevic.

"They said it was quite a sombre occasion and obviously quite sad: we still don't know who this person is," said Detective Inspector Paul Arnold, of Flemington Local Area Command.

ABC reported Bridget was only about one-or-two-days-old at the time of her death, and she has the features of a south-east Asian.

Detective Inspector Arnold also renews his appeal for Baby Bridget's mother and family to show up.

"It's not to arrest and charge the mother with any type of offence... It's to try and give the mother and the family closure... That's all we want," he said.

A small group of police and a few locals showed up at Rookwood Independent Cemetery in southwest Sydney to lay Baby Bridget to rest.

The investigators have looked into forensic tests, CCTV captures, and they have made relevant inquiries to hospitals interstate. But Baby Bridget's story remains a mystery.

Anyone with information may contact 1800 333 000.