Sanft, 26, is charged with manslaughter and has pleaded guilty to unlawful possession of a pistol, as the sawn-off shotgun was technically classified.
He is on trial in the High Court at Auckland before a jury and Justice Geoffrey Venning.
During crown prosecutor Katie Hogan's opening address today, she said: "There is no evidence that the gun fired accidentally."
The day before Amokura died Sanft's elder children were clearing out a hot water cupboard at the house when they found a sawn-off shotgun wrapped in a purple sheet, Hogan said.
Sanft did not have a secure gun safe at the home nor a firearms licence, she said.
The next day as the family prepared to move homes, Daniels left to hire a skip bin, leaving the four children at home with Sanft and another.
About 11.30am some friends of Sanft and Daniels arrived to help with the move.
One of the men told police that when he arrived Sanft was in the driveway "holding a sawn-off shotgun with both hands", Hogan said.
She added Amokura was "playing up" and jumping on the couches in the driveway.
"[Sanft] became angry and pointed the gun, perhaps intending to only scare her," Hogan told the court.
Sanft then pulled the trigger, she said.
Amokura was shot just above her left eye at "close range", causing a "significant and unsurvivable head wound", Hogan said.
A "distraught" Sanft immediately dropped the shotgun to aid his wounded daughter, she added.
Three police vehicles, which happened to be driving past the address to another incident at the time, were waved down.
"The scene that police arrived at was chaotic and traumatic," Hogan said.
During the distressing scene Sanft also made a series of remarks to police, she said.
"I pulled the trigger, she was just playing up, I f****d up, what have I done?" Hogan said Sanft told an officer.
"I shot her, I shot her."
Hogan said Sanft's 5-year-old stepson also witnessed the incident and told an officer that "dad was angry".
Sanft also told an ambulance officer, "I don't want your sympathy" and "I'm a killer", Hogan told the jury.
She said Sanft also mentioned to police he was less than a metre from his daughter when he fired the gun.
Family friend Anna Leao, who was helping Sanft's family move homes, recalled hearing a bang. She then witnessed the tragic aftermath.
"That's when I realised that Amo had died," she said, battling through tears, as Sanft also broke down in the dock, breathing heavily, tears rolling down his face.
She remembered seeing Sanft "sobbing and calling [Amo's] name" while cradling his dead child, but had not seen him earlier handling the shotgun.
Leao described the shock of the situation as she attempted to help, calm the other children, and call 111.
"I didn't know what to say, I didn't know what had happened. I didn't want to tell them something I didn't see or hear. All I said was that we needed an ambulance officer," she said of the emergency call.
A recording of the 111 call, one of four Leao said she attempted to make, was then played to the court.
"I have no idea, my niece is laying on the ground bleeding [sic]," Leao told the operator.
"You need to send the ambulance - I don't even know what happened," she said before ending the phone call.
She was also seemingly haunted by one horrific memory.
"On the top of my head there was a bit of her skull," she told the court through anguished tears.
"We couldn't hear her voice any more."
Leao's husband, Jimmy Tikoinamaka, who has been a friend of Sanft's since the pair were in their early teens, also gave evidence.
He recalled seeing Sanft with the gun tucked into the front of his pants and also clutching it with both hands.
The Crown earlier told the court how the firearm had been modified, both the barrel and wooden handle had been sawn off, and the serial number ground off.
The shotgun was 1.98kg and 450mm long, and therefore technically classed as a pistol.
The gun, a Norinco JW87 12-gauge single-barrel shotgun, was loaded with one Winchester buckshot round in the chamber.
It was seized, examined and tested by police.
Police fired 12 test shots and on four of the shots the gun failed to fire, Hogan told the jury.
The armourer noted that the shotgun most likely failed to fire when the trigger was pressed "gently", Hogan said.
The Crown alleges that Sanft was responsible for his daughter's death - but that he never meant to harm her.
Defence counsel Phil Hamlin said in his opening address that the gun had fired accidentally.
"He caused the death of his child, the own flesh and blood of his daughter, but it was an accident," he said.
"The shotgun fired accidentally without having to have pulled the trigger."
He said Sanft did not believe the gun was loaded and did not "point the gun at her or at her head".
He said Sanft never used the weapon "in any anger, annoyance, frustration" as the Crown alleges.
"Tragically his daughter was killed instantly," he said, but added the gun was faulty and "unsafe".
"Mr Sanft does not get the blame for the killing of his daughter, the gun does.
"He didn't realise it has these unsafe features."
The trial has been scheduled for three weeks.
