A mother whose daughter died from a case of Sudden Unexpected Death in Infants (SUDI) has recalled wishing an ambulance would "hurry up" after waking to find her baby unresponsive.

Key points: The parents found their three-month-old daughter unresponsive two days before Christmas

The parents found their three-month-old daughter unresponsive two days before Christmas The father told the court he attempted to perform CPR

The father told the court he attempted to perform CPR The parents were unable to find resources to explain the loss to their two older children

The NSW Coroner is investigating the unrelated cases of a baby girl and boy who died in December 2012 and July 2014, respectively.

The little girl, aged three months, was described as "a great baby" by her mother and was assessed as being "well and happy" by a doctor nine days before her death, despite some feeding issues.

She was found unresponsive by her father two days before Christmas, who then called paramedics and woke her mother.

"I saw [her] and the colour," the mother told the court.

"The way her eyes were, I knew in that moment she was already gone.

"At that time I just ran out the front and waited for the ambulance to arrive ... just hoping they would hurry up and hoping there was something they could do."

The father told the coroner he attempted to perform CPR.

"I was in a state where I was believing I was doing something in regards to it until paramedics pulled me away and told me she had been gone and there was nothing I could do," he said.

The court heard it was a warm day and the baby slept in a "woombie", or body-sized sleeping bag, inside a cradle.

The father told the court his daughter appeared to be "clammy" when he found her.

Both parents agreed they struggled to find resources to help explain the loss to their two older children.

"My concern first and foremost was how to explain it to them," the woman said, adding that eventually the couple found a range of books which helped.

The mother said paramedics were unable to revive her daughter. ( ABC News: Dan Cox )

In both cases, the cause of death wasn't able to be determined.

The baby boy was also assessed as being well weeks before his death.

He slept in a bassinet and was wrapped in accordance with hospital guidelines.

Coroner Teresa O'Sullivan told the families the process would not be easy.

"Just know you've got all of us on your side, we're all very much aware of how difficult this is for you all," she said.

"I don't think anyone will lose sight of the fact of what we're really here for, and that is your two beautiful babies."

The inquest continues.