The woman, a neighbour who asked not to be named, said she had never seen 28-year-old Jie Smith before he appeared on her New Lambton doorstep with a lifeless child in his arms.

Mr Smith, who faced court on a murder charge on Thursday, had been standing in the street calling for help before he approached the woman’s house at about 4.30am Saturday.

“I came out and saw the baby in the man’s arms,” she said.

“He was sitting under the rail [on the verandah]. I panicked, rang the ambulance and told the ambulance what I was seeing. They asked me to check his airways and I couldn’t feel anything.

“They told me to start CPR and [the triple zero operator] talked me through it, I’ve never done it before.”

She tried to revive the baby until paramedics arrived.

“‘Please don’t die. Come on little man’, that’s what I kept saying,” the woman told the Newcastle Herald.

“The man was just standing there saying ‘come on buddy, come on buddy’.

“He never told me anything, I never asked anything. I was just too worried about trying to save the baby."

Read more: Man charged over alleged baby murder

The boy was taken to John Hunter Hospital in a critical condition, where he died late on Sunday from what a post-mortem determined to be a traumatic head injury.

Mr Smith did not enter pleas to charges of murder and reckless grievous bodily harm when he appeared briefly in Wyong Local Court on Thursday morning.

Police said Mr Smith had been in a relationship with the baby’s mother for about six weeks, but she was not at the Fairfield Avenue home when the child was allegedly fatally injured. The baby and his mother cannot be identified for legal reasons.

Detectives from Newcastle police district and the State Crime Command formed Strike Force Wandearah to investigate the baby’s death.

They arrested Mr Smith at Budgewoi on the Central Coast on Wednesday afternoon and charged him.

Dressed in a camouflage singlet and board shorts, Mr Smith stood in the dock on Thursday as Magistrate Elizabeth Ellis advised him he would be foolish to apply for bail. 

He did not apply for bail and it was formally refused. 

A brief of evidence will be served by April 11. The matter was adjourned to Newcastle Local Court for mention on May 1.

Read more: Court and crime news

Two women, believed to be relatives of the child, left the court accompanied by a Salvation Army officer.

Newcastle police commander Detective Superintendent Brett Greentree made a statement from the NSW Police headquarters in Sydney after Mr Smith’s court appearance, saying the child’s death was “tragic”.

“The allegations are certainly horrific,” he said.

“It’s a tough job at the best of times for police ... but these types of incidents really test the resolve of first responders.”

Detective Superintendent John Kerlatec said the child’s father was “very distraught” and that nobody “could begin to fathom the emotional trauma” the boy’s mother was going through.

“It affected everyone who turned up at that location, it affected the hospital staff, the ambulance staff … it's horrendous,” he said.

“It was a very difficult investigation for the people responding, for the emergency services that responded, for the investigators, due to the age of the child.

“We owe it to all children to look after them."

A Go Fund Me page has been set up online to raise money for the six-month-old’s funeral expenses.

The woman who performed CPR on the baby said she was “devastated".

“I’m not sleeping much. I still see his little face there on the floor, I’m sorry to say,” she said.

“It’s just horrible. I feel so sorry for the mum and the father that lost their baby. They must be going through hell at the moment. 

"I’m sorry I couldn’t do any more to help - I tried.”