Sandip Adhikari, 27, appeared in court on Wednesday for the first time since being charged with negligent driving occasioning death.
The young girl was struck outside her home in Auburn, in Sydney's west, about 2pm on Tuesday.
CCTV footage of the incident, seen by AAP, shows the girl sitting in her driveway and playing on a sunny afternoon.
An SUV turns into the driveway, strikes the preschooler and continues for a moment before stopping.
The footage shows the driver checking underneath the car and becoming visibly distraught when they see a small body there.
Paramedics treated the girl at the scene.
She later died in Westmead Hospital.
Adhikari was taken to another hospital for mandatory testing and then charged over the incident.
He faced Burwood Local Court on Wednesday for the first mention of his case, which was quickly adjourned to a later date.
Adhikari has not entered a plea to the criminal charge.
But outside court, he told reporters he was "really sorry" as he tried to shield his face from the cameras.
His lawyer Danny Eid said Adhikari was "very, very stressed and worried" about the girl's family and their welfare.
"This is a very, very sad case," he said.
"He's asked me to relay his deep sadness to the whole family who have lost their beautiful young child."
When asked if Adhikari had spoken to the girl's family, Mr Eid said it wouldn't be appropriate for his client to contact the family directly.
"(He's) very saddened. Very stressed about what occurred," the lawyer said.
"His whole focus is on the welfare of the family of the deceased."
Adhikari will return to court in October.
Until then, he is on bail under strict conditions which include reporting to police every day.
The 27-year-old is also barred from operating a motor vehicle while on bail.
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