A Counties Manukau police spokeswoman said despite the good leads, police still wanted to hear from anyone with information.
It keeps replaying through Ben Scott's head - the image of a stranger running out of his bedroom, flipping the bassinet where his 11-week-old son was sleeping and sending the infant flying on to the floor.
"It's just that picture ... the image of my baby's bassinet on its edge, then falling backwards. It's terrifying," he said.
Mr Scott was woken at 5.25am on Sunday by his fiancee, Chelsea, screaming.
As they slept, at least one person had broken into their Manurewa home and made their way through each room stealing whatever they could carry.
"She was screaming 'get out of my house you mongrel'," Mr Scott told the Herald.
"I leapt up and just saw the back of someone's legs running out of our bedroom."
Mr Scott took off after the man, who reached over and pushed the bassinet in which the couple's baby son Carter was sleeping.
Little Carter fell to the floor and Chelsea ran to him as Mr Scott tried to catch the intruder.
He followed the man through the house and out on to the street, just in time to see him take off in his Ford Ranger truck.
"At that point I thought 'do I risk jumping on the windscreen?' But I thought it was more important to go back inside and see if my kids were okay," Mr Scott said.
His elder son Coen, 7, and Chelsea's nephew were in a bedroom down the hall when the burglary happened.
"It was when I got back inside I started to realise how extensively these guys had been through our house," Mr Scott said. "What they took was ridiculous."
The thieves took another car from the property, and cleaned out the family's televisions, laptops, iPads and a tablet Coen was given for Christmas. They also took credit cards and a significant amount of Chelsea's jewellery.
"They took the TV off the wall in our bedroom, within two metres of where I was sleeping. They took my jeans, jackets, hats, some bottles of booze."
The spare key to Mr Scott's Ford was hidden in his sock drawer, which they rifled through. They also took his cellphone which he keeps under his pillow while he sleeps.
Chelsea's phone was also sitting close to her pillow and as one of the thieves reached for it, she woke up.
"It is frightening how long they were in the house while we were asleep. They went into Coen's room and unplugged a laptop and took it from right beside his bed.
"We found their shoes, they left them at the top of the driveway. Obviously they knew they would make less noise in just socks."
Mr Scott said baby Carter was not injured and didn't appear to be traumatised by his ordeal.
"He's doing good. Coen's a bit upset because they took his Christmas present. And we had been at the beach the day before so the new boogie boards and all the beach toys were still in the car and they are gone.
"My fiancee will be scarred by this, the baby is fine but it's a terrifying thing to see."
Mr Scott has lived at the house for 12 years, three of those with Chelsea. He had never been burgled or had anything untoward happen in that time.
"Going on what they stole they must have been in the house for about half an hour. When I look at how detailed they were at going through the house, it's creepy. Who goes through a sock drawer?
"The material stuff, I couldn't give two s**ts about. But they've scared my family. They are mongrels, there's no doubt about that."
Mr Scott had a message for the offenders.
"You threw my baby. You've destroyed our privacy and what we perceived as being our safe place. You didn't just break into a house, you've done more than just take people's s**t."
Mr Scott urged anyone who had information about the burglars to contact the police.
"Having these people locked up will make us feel a lot better," he said.
Manukau central area prevention manager Inspector Bruce O'Brien said one of the vehicles stolen was found dumped on the North Shore yesterday.
"We will be doing a forensic examination of that vehicle to help us with the investigation," he said.
Yesterday, police released images of a woman they hoped to speak to in connection with the investigation.
The woman has now been identified - and police hope she will be able to provide information that can lead to the offenders.
Anyone else with information on the burglary is urged to come forward.
"It is pretty concerning that these offenders have broken into somebody's house in the middle of the night and have obviously been searching around the family as they slept.
"And, when they have been disturbed they have pushed a bassinet where a young child was sleeping. It's very lucky we haven't got an injured baby ... it's terrifying."
Can you help?
If you have information about the burglary contact the Counties Manukau police on 09 261 1300. If you want to pass information on anonymously call Crime stoppers on 0800 555 111.