While Molia and his partner had been separated "for quite some time" after the incident, mainly due to bail conditions, the judge noted that had "now been sorted out".
But he noted the imbalance in power in Molia's favour.
"You are a physically large man and potentially your baby was at real risk of your violence on this occasion when you were disinhibited by alcohol.
"It was serious and happened because I suspect you had drunk too much.
"Young men drinking too much is never a good look and I suspect Mr Molia that you have repeatedly, since the day, wanted to go back to a time before that to have not made the decision to strike out at your young son."
In assessing Molia's application for a discharge without conviction, through his lawyer Roger Laybourn, Judge Cocurullo said he needed to identify the gravity of the offending and then assess the direct and indirect consequences on a conviction on him and whether that would be out of proportion.
He noted that Molia was from a large Tongan family in South Auckland before he shifted to a school in Waikato.
He was a talented rugby player; having been chosen for the Waikato under 18s, under 19s and this year under 20s. He was a talented theatre actor - playing the lead role in a school play - and was a singer in the school choir.
Laybourn told the Herald Molia was highly respected at his former school, St Pauls, where he was seen as a mentor and a "very caring and very protective" person.
About two months prior to the incident, Molia's beloved father had died.
While there were eight siblings, of whom Molia was the youngest, he was particularly close to his father, who keenly followed his rugby.
He then tried to deal with his father's death "by himself" and on that night, had been drinking, came home, his partner was angry with him and the child was crying, when he slapped him.
"Everyone accepts that they were mild blows," Laybourn said. "But he knew it was wrong ... he's never suggested that it's parental correction."
While on bail, Molia had made good progress with grief and alcohol counselling, so much so the condition not to see his partner was eventually dropped.
As for his rugby talents, Judge Cocurullo said while "there was a high notion of you being a promising rugby player, for me it is this notion of your travel".
"Whilst one might say that your sports manager is not person expert and versed in immigration matters [he] probably brings some experience about travel in that respect but equally away from rugby I well understand that travel may be a real difficulty for you."
He described the offending as "moderately serious" but also that Molia is young himself with a young child and a first offender.
His children would grow old and a conviction could impact on his ability to go on school camps.
Molia was not yet under a professional rugby contract and working as a storeman and noted he had a promising future.
"You are a talented young man with a bright future and I say that not just because you are a good rugby player, I say that because you are a talented young man in other things."
Judge Cocurulla said while he didn't want to minimise what happened, he was prepared to use his discretion and grant Molia's application.
Asked about criticism of a judge wiping another sportsman's conviction for drunken behaviour, Laybourn said the basis of the decision wasn't purely about his sporting prowess, rather his promise and broader character as a person.
The incident was out of character and he'd submitted references to the judge showing that, and he'd taken steps to deal with his father's death.
