Road policing Sergeant Kevin Stewart said all indications were that Mr Singh had lost control of the van while it was going down a hill about 80km from Napier.
The van plunged 15m down a cliff and "pancaked" upside-down.
"Early reports that he was ejected from the van were incorrect. It appears he was at the bottom of the cliff with the rest of the occupants and he managed to climb out of the wreck, cradled the 5-month-old baby and walked through some pretty thick bush until he was able to get back up on to the road to wave down some passers-by," Mr Stewart said.
"The experienced road policing staff that were there, all of us to a man, are amazed that there were no fatalities considering the location where the van ended up and the condition of the van."
Once the 33-year-old made it back to the road and waved a motorists down, he passed Manmeet to a motorist then collapsed due to his injuries.
"He's still a sick man, full credit to him for raising the alarm because if he didn't, who knows how long they would have been down there."
Investigations were continuing but police had no reason to believe speculation Mr Singh had fallen asleep at the wheel because it was believed he had only driven the van from Taupo, Mr Stewart said.
Sikh priests were called to the hospital to administer recuperative prayers to baby Manmeet and his father.
Gurmeet Singh, a former Sikh priest who has been helping out at the Ravidas Temple in Hastings, said he and another priest were called to the hospital on Thursday to pray for the victims.
"The family are traumatised. It was a serious crash ... sometimes it happens, we make mistakes. The family is quite close to me.
"We gave prayers to help them get better, to help for their recovery and with ongoing support," he said.
The five Melbourne-based family members were in New Zealand to celebrate the birth of Manmeet, the first son in the family.
They had been collected from Auckland Airport by Mr Singh and the two Hawke's Bay family friends. The eight was heading back to the Bay when the van ran off the road.
Mr Stewart said the crash was a reminder of the need for extreme care when driving the SH5 between Napier and Taupo.
"The Napier Taupo highway is a beautiful road to travel - the scenery is fantastic - but it's the kind of road that if you get it wrong it will bite you, and it bites you very hard. We cannot stress enough that people who drive that road have got to be fresh, they've got to be alert, watch speeds and following distances because that road can be very, very dangerous."