Antoinette Campbell, 23, was indulging her selfish wish "for a bit of freedom" when she left her baby, Desrae, to see her boyfriend.
But the court was told how doctors could not agree on the cause of the baby's death and that she could have fallen victim to cot death syndrome.
Campbell was put on probation for three years on condition she lives at a bail hostel.
The Recorder of London, Sir Lawrence Verney, told her: "This is an opportunity the court will not be able to repeat."He said it was clear from numerous reports that people wanted to help Campbell and the court wanted to help too.
Campbell had admitted child cruelty at an earlier hearing and was remanded for reports.
Her plea of not guilty to the manslaughter of her baby was accepted by the Crown after Mark Dennis, for the prosecution, said doctors could not agree on the cause of death. Although a pathologist had found signs of dehydration and starvation, two paediatricians disagreed these factors were the cause of death.
They decided the baby had died only a few hours after her mother had abandoned her at her council flat in Kilburn, north-west London, either from cot death syndrome or metabolic disorder. Mr Dennis said it was impossible to quantify how much the stress of abandonment had had on these natural causes of death.
When the baby died Campbell left her early on Friday evening and went to visit her boyfriend, the baby's father. She pretended to him her mother was looking after Desrae.
Campbell stayed the night and did not return to her own home until late on Saturday night, after visiting another friend on the way home.
Campbell admitted to police she had abandoned her baby. She said she had only intended to stay for a while at her boyfriend's because he had complained in the past about her not getting a babysitter.
"When she [Desrae] wasn't there it was providing her with a bit of freedom, a bit of space, a bit of thinking time. She admits it was no excuse and that she was being selfish in all she has done," Jeremy Dein, defending, told the court.Reuse content