The 22-year-old man, who cannot be named for legal reasons, is accused of grabbing the seven-month-old boy around the waist and ‘‘vigorously’’ shaking him about 9pm on Tuesday after getting frustrated when the child would not drink his bottle.

The man’s alleged actions were witnessed by family members living with him and the child in a house at Warrawong.

The child was taken to Wollongong Hospital on Wednesday suffering serious injuries, including chronic bleeding on the brain.

He was later transferred to Sydney Children’s Hospital at Randwick where he remained in a critical condition on Thursday night.

The man was denied bail in Wollongong Local Court on Thursday on a single charge of recklessly inflicting grievous bodily harm.

Prosecutor Kylie Talty told the court the hospital had advised police on Thursday afternoon the boy had ‘‘poor prospects of recovery and survival’’.

Sergeant Talty said the man’s current charge could be upgraded if the child died from his injuries.

Police documents outlining the case against the man said he told police he’d been playing video games on Wednesday in the bedroom he shared with the boy when the child let out a sudden high-pitched scream.

The man picked his son up, however the child’s limbs went stiff and he screamed a further five times, the documents said.

He noticed the child  gasping for air and he called triple-0, which directed him to begin CPR.

Ambulance officers arrived a short time later and found the boy in cardiac arrest.

He was immediately taken to hospital, where staff noted he was showing several signs associated with a brain injury.

A CT scan revealed the boy had bilateral subdural haematomas, requiring staff to drill holes into his skull to relieve the pressure.

During an interview with police on Wednesday evening, the man said his son was sick the previous day. However, he’d taken him to a doctor in Warilla to get his baby injections before returning.

He allegedly told police the boy had been fine when he went to sleep but woke up on Wednesday morning crying and unsettled.

He said later that day when he was playing video games the boy began to scream and became stiff.

He denied accusations he shook the baby.

However, the court on Thursday heard investigating officers had collected signed statements from some of the man’s family members who saw him pick the child up on Tuesday evening and violently shake him for approximately 10 seconds, while yelling ‘‘Shut the f--- up you little f---ing faggot’’.

In court yesterday, the man’s lawyer, Jonathan Kearney, said his client had moved to Australia from New Zealand six months ago to be with his then partner and child, however the boy’s mother had returned to New Zealand three months later and left the man to take care of the child.

Mr Kearney said the man had no criminal record in Australia or New Zealand and would agree to strict bail conditions including surrendering his passport.

However, magistrate Susan McGowan refused to release the man, noting the ‘‘alarming’’ nature of the case against him, which she said appeared to be a strong one.

She also acknowledged that the man might face further charges at a future date if the child did not survive.

The matter will return to court early next year.