Judge Rea told the court that between June 5 and July 16 last year Roberts had been in a relationship with the child's mother.
The pair lived at the same housing complex and Roberts would spend most nights at the woman's house.
He was also involved with the "day to day care" of the child, the summary states.
"The defendant was also trusted to have sole care for the victim when her mother was away from the home. This would occur almost daily."
It was noted in the summary that before their relationship began the child was free of marks and bruises.
"She could be described as a healthy, happy child."
Near the end of June, bruises began appearing on the head and face of the victim - they were noted and discussed with Roberts and the family.
Judge Rea told the court a number of theories were put forward as to how the child innocently became hurt such as "banging her head in the cot".
None of the theories put forward were ever physically seen happening.
On July 15, an argument erupted between Roberts and the child's mother.
He left the home but returned for the night.
The next morning, Roberts took the child from her cot to see her mother but the pair became embroiled in another argument.
He left the address only to return a short time later.
"At this point the victim was her usual self and was alert and conscious," the summary says.
Roberts was alone with the child while her mother showered, the only other person present was the child's 5-year-old half-sister.
After he saw the child's eyes roll back and her body going floppy while dressing her, he "ran carrying the unconscious victim to the medical centre" which was across the road.
After an examination she was found to be unconscious, "fresh bruising was noted on her back, and on the right hand side of her face and her right ear". A CT and MRI scan revealed a small sub-dural haemorrhage on her brain.
Medical expert opinion was that the brain haemorrhage and loss of consciousness happened "simultaneously", the facts state. The summary states while Roberts had the child in his care he caused the injuries.
His comments were that he "would not hurt a child".
But he did not offer an explanation for how she was injured.
"You are very fortunate indeed that this child has made a full recovery," the judge told Roberts.
The judge said he made small discounts for Roberts' inexperience, youth and his guilty plea.
The plea was entered after being given a sentencing indication and for this reason Judge Rea said Roberts showed no remorse for his offending.
He was also handed his first strike under the three strikes law.
