Paramedics found Ellie Butler lying beside a low child's stool at her home in Sutton, south-west London.
Her father Ben Butler claims she fell, but the prosecution said her injuries were caused by being thrown against a wall or hit with a "blunt weapon".
The 36-year-old denies murder and a separate charge of child cruelty.
At the Old Bailey, prosecutor Ed Brown QC said a post-mortem examination revealed the child suffered skull fractures from at least two severe impacts.
Read more updates on this story and other news from London
He said the doctor who carried out the examination and a neurological pathologist agreed her injuries were unlikely to have been caused by an accidental fall.
A third expert, a forensic pathologist, believed Ellie's major head injury was "the result of one or more very forceful blunt impacts, arising through being thrown against a wall or the ground, or struck with a heavy blunt weapon", the court heard.
"A domestic accident could not have given rise to these complex, catastrophic and rapidly fatal injuries," Mr Brown added.
The court has heard how Ellie's parents, Mr Butler and Jennie Gray, summoned an ambulance two hours after her injuries were believed to have been caused.
Mr Butler and Ms Gray, also 36, deny child cruelty over an untreated broken shoulder Ellie suffered weeks before her death.
Ms Gray has admitted perverting the course of justice.
Mr Brown told jurors it was a "distressing case" of a father accused of murdering his daughter and failing to seek medical help for her earlier injury.
Ms Gray had been "determined and persistent" in trying to protect him by hiding and destroying evidence, he said.
On the day of Ellie's death, on 28 October 2013, Mr Butler and Ms Gray exchanged a series of phone calls and texts, records show.
He tried to call her at her office at 12:46 but reached a voicemail message and sent a text asking her to "answer".
Her colleague Tracey Bernstein said in a statement that the way Ms Gray got up and left the office was "just not right".
Another former workmate, Victoria Harris, said she had seen Ms Gray looking "agitated" on the phone. "It did appear to me it was more than just a secret conversation," she added.
Minutes later Ms Gray was caught on CCTV dashing out of her office, near the Old Bailey.
She sent a text to her manager to say she had left for home as she was "feeling unwell".
But taxi driver Derek Greenwood, who drove her back to Sutton, overheard her on her mobile phone saying loudly "you have done what?", "you have gone where?" and "you're joking".
The court also heard from their neighbour, Lucy Jackson who recalled hearing arguments and a raised male voice coming from their home.
Jurors have previously been told that Mr Butler has had a conviction for assaulting Ellie as a baby quashed. Her parents then won a High Court ruling to return her to the family from foster care.
The trial continues.

The motto Nil Satis Nisi Optimum, which means "nothing but the best is good enough", dates back 75 years but disappeared as part of a redesign.
The club apologised in May after 22,000 fans signed an online petition condemning the "awful" 2013-2014 badge.
Fans can vote on three new designs on the club website from Monday.
Club communications director Alan Myers said: "There were clear messages that have come out from fans as to what they want.
"The motto Nil Satis Nisi Optimum will be on the new crest because 95% to 96% of fans said they want it and that's what we wanted."
Everton consulted more than 200,000 fans and also players following criticism of the "embarrassing" new crest.
The club said one fan travelled from Spain to Goodison Park to have his say about the redesign - even though he was advised an online form was available.
The new crest ideas will be unveiled on Monday 23 September.
A six-year-old girl's "catastrophic" head injuries could not have been caused by an accidental fall, as claimed by her father, a court heard.
[NEXT_CONCEPT]
Everton FC are to restore the club's motto to their crest after its removal prompted outrage from thousands of fans.