The country was in an alert level 4 lockdown at the time in a bid to combat Covid-19.
Inside the Papatoetoe home Dean became angered that baby Thalia would not stop crying.
According to court documents, he wanted to be the kind of father who could settle his baby and in frustration that he could not, suspected she was not his.
Dean struck the baby at least five to six times with a closed fist. He later told police that on a scale of 10 the force he had used was a seven to eight, similar to "jabbing" an adult in a boxing match.
Dean was interviewed by police on April 18 and 19.
In the first interview, he claimed Thalia had stopped breathing as he was rocking her in his arms.
When challenged with the physical evidence his story changed.
Dean accepted that he had caused Thalia's death but denied any intention to hurt her.
In the second interview, he admitted striking her on the head five to six times, possibly more.
She had stopped breathing, her body becoming loose.
Dean immediately put her down and began CPR. The girl's mother called for an ambulance.
The ambulance officers were told that Thalia had displayed flu-like symptoms and fever in the week leading up to her death.
She was declared dead in Middlemore Hospital about 7.40pm.
At that stage, the cause of her death was not known. Because of the report of flu-like symptoms, the death was initially treated as a possible Covid-19 case.
A post-mortem examination undertaken on April 16, showed the preliminary cause of death was blunt force injuries to the head.
Those listed injuries included the finding of about 25ml of blood in the bilateral subdural region.
'I did it but I wasn't thinking'
According to court documents, Dean had felt like his head was going to explode because of the crying.
Dean told police: "I knew those hits was going to cause, you know, some damage but it's just 'cause I'm angry, I'm frustrated, I'm not thinking right and then I'm just you know, I wasn't thinking at all. I did it but I wasn't thinking."
Dean, who was represented by Marie Dyhrberg QC, has been remanded in custody until sentencing on May 4.
Justice Fitzgerald also gave Dean a warning under the three-strikes law.