The defendant, on trial for murder, had been receiving help under a court care order to look after the child at her home on Slater Lane, Leyland, Lancs.
But an hour and 20 minutes after her support worker left the property at 11pm on April 19 last year, Crichton rang 999 for an ambulance reporting her daughter was not breathing, Christopher Tehrani QC, prosecuting, told the court.
The jury heard an ambulance was called 20 minutes past midnight and paramedics managed to resuscitate Amelia on her way to the Royal Preston Hospital but she was then immediately transferred to The Royal Manchester Children's Hospital for specialist treatment.
Two days later doctors concluded Amelia would not recover from her "catastrophic" brain injuries and further life support was withdrawn at 8.15pm on April 21 last year, with the child declared dead 20 minutes later.
She had been born on September 8 2016, at between 23 and 24 weeks, and if she had been full term would have been just four months old at the time of her alleged murder.
Weighing just 570 grams on delivery she was born "on the cusp of life" and did not leave hospital until March 23 2017, receiving six months of treatment for various complications of her pre-maturity.
But after discharge she behaved like a normal baby, going home to live with the defendant under a "care plan" with the help of support workers who stayed overnight at the address until the hours were reduced over time.
Around 6pm on the night Amelia was allegedly murdered, a care support worker arrived at Crichton's home.
During the evening when the support worker suggested Crichton take over feeding the child, the mother replied: "No, you do it," and went outside for a cigarette, the court heard.
At 11pm the care worker left and Amelia appeared to be fine, until, an hour and 20 minutes later, Crichton rang 999 for an ambulance.
The defendant's claims that the child had simply collapsed were shown to be discredited by expert medical examination of her injuries following her death, Mr Tehrani said, which excluded any accident, natural disease or medical condition as an explanation.
Tests showed Amelia had suffered a skull fracture and bleeding on her brain, with Crichton offering no explanation as to what had happened.
Expert medical analysis of her body concluded she had been the subject of a "violent physical assault" immediately before her collapse as a result of "striking or throwing" against a hard surface as well as bodily shaking, the prosecutor said.
Injuries included bleeding to the brain, damage to nerve fibres in the brain stem, a complex skull fracture to the right side of Amelia's skull and bleeding to her right eye.
Medical experts concluded the injuries were "strongly supportive" of being due to a "deliberately inflicted head injury" caused by "significant blunt force".
Crichton, who denies murder, was arrested four days after her daughter's death.
She told police Amelia had been asleep in her bouncy chair but let out "an almighty scream" so she picked the child up and her daughter went "limp".
She denies murder.
The trial continues.