Judge Howard Llewellyn chaired a significant case review into the death of Alexis Matheson who was attacked by Mark Simpson at the home he shared with the baby's mother in Aberdeen.
Alexis died in hospital in Edinburgh on December 10 2007, less than two months after being born
Simpson was charged with assaulting her on various occasions between November 8 and December 9 by seizing hold of her, shaking her and compressing her chest, leaving her so severely injured that she died.
He was found guilty of her murder and was jailed for life in November 2010, being told that he must spent at least 20 years in prison.
In the significant case review, Judge Llewellyn considered if the baby's death could have been prevented had signs of non-accidental injury been detected earlier.
"I conclude that her death was not predictable from the information available to practitioners," he said.
While he concluded that Alexis's injuries may have been treatable in the few days before her death, he said: "Her survival was possible rather than probable. I do not therefore conclude that her death would have been prevented."
The review took place after Lord Uist, the judge during Simpson's trial, said that some of the evidence gave him serious concern about how the health service dealt with Alexis and whether her death could have been prevented had her injuries been spotted earlier.
Lord Uist said at the time that it was a matter of concern that Alexis's mother, Ilona Sheach, sought a doctors appointment because she was seriously worried about her baby's health, but was offered one only for the following week.
Alexis was seen by a doctor on November 29 2007 but "nothing was done about possible signs of non-accidental injury", Lord Uist said.
"Whether the death of baby Alexis could have been prevented had she been so referred is a matter which, in my opinion, merits a very full inquiry," he said.
The significant case review was held to determine whether lessons could be learned from the case.
Judge Llewellyn concluded that NHS staff are "committed and hard-working professionals who aim to deliver the best service they can to the public".
There is "no evidence to indicate there were significant or mounting concerns being expressed by anyone" over Alexis's health or Simpson's involvement with the baby, he said.
Judge Llewellyn said he found no evidence of significant staffing difficulties within either the midwife service, the health visiting service or the GP practice that Alexis was seen at.
But he recommended that the telephone appointment system operated by GPs be reviewed so that in future it can be determined if the patient is a baby and who should then be given an appointment within 24 hours.
The practice of prescribing drugs over the telephone for new-borns should also be reviewed because a GP's ability to diagnose an infant's needs is "inherently inhibited" by not being able to see them, the judge said.
Doctors should always consider physically examining young children and if they decide not to do this, they should record their reasons for doing so.
He also recommended that the training of GPs and health visitors be reviewed to ensure they can recognise the signs of non-accidental injury.
NHS Grampian has already introduced changes in the wake of Alexis's death.
Communication between health visitors and GPs has been improved and they have been provided with better child protection training, the health board said.
It is also working with Robert Gordon University in Aberdeen to develop child protection in nursery and midwifery education.
Elinor Smith, director of nursing at the health board, said: "This is an important report. It attempts to constructively identify institutional weaknesses and so is more helpful in learning lessons for future practice than concentrating on fault finding.
"I welcome Mr Llewellyn's conclusion that all professional NHS staff were committed to delivering the best service and that the midwives and health visitors sustained a proactive approach to maintaining contact with mum and baby.
"I note the report finds no evidence of staffing difficulties within the midwifery, health visiting or GP services and that the actions taken by the health visitors were persistent and professional. It also highlights the availability of advice for second opinions from the Royal Aberdeen Children's Hospital.
"Although the report concludes that it is unlikely Alexis's death could have been prevented by the intervention of NHS staff, it does contain eight recommendations about telephone appointments, the recording of physical examinations, training and monitoring, and liaison between GPs and health visitors.
"NHS Grampian has already actioned many of the recommendations but others require more detailed planning over a longer period.
"The improvements being made will benefit children in the future."
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