There was a purple bruise on the child's jaw, and two oval-shaped contusions on the front of both shins were discovered as paramedics fought desperately to save her life.

The child, whose name has been suppressed, died that afternoon.

But the bruising was not present during a health check by nurses the previous day, an inquest heard on Monday.

A police officer told the inquiry that suspicion immediately fell on the parents. Listening devices were installed in the home within a fortnight of the death, but no charges have been laid.

Intensive-care paramedic Warwick Finch was sent speeding to a Gordon home about 5am on the morning of August 18, 2012, in response to a priority one emergency. Mr Finch entered a home to discover the "flaccid, grey" child on the lounge.

He said she was not breathing, had a slow heart rate and would not respond to stimulus.

"She looked very sick," Mr Finch told the inquest.

He began CPR and rushed the child to the Canberra Hospital for treatment.

Mr Finch said he heard an explanation that the baby had been injured after falling off the lounge while seated with her father.

But he could not recall if he was told by the family at the scene or by the triple-0 operator while on route.

Coroner Bernadette Boss is investigating the circumstances that led to the child's death.

Counsel assisting, Shane Gill, said the inquest would have little trouble finding the infant died of a brain injury.

But he said the difficulty was determining how and when the injury was inflicted, and who caused it.

The court heard the girl spent the first four weeks of her life in hospital after she was born prematurely in June 2012.

Ill health forced another four-week hospital stay before she was discharged in mid-August.

Two nurses from ACT Health's Newborn and Parent Support Service, who visited the Gordon home on August 17, reported the child had been feeding, had put on weight and showed no signs of injury or bruising.

One of the nurses told the inquest she had been surprised to see the family at the neonatal intensive care unit the following day as she had seen no indication the baby was ill.

The police officer told the inquiry the listening devices, installed in the family home, were monitored for three months.

Mr Gill requested the officer be stood down from the witness box, but said he would be recalled later this week.

The inquest before Dr Boss continues on Tuesday.