Marvyn Iheanacho, 39, is accused of causing Alex Malcolm fatal head and stomach injuries during a violent assault on the evening of November 20 last year.
Witnesses heard a "child's fearful voice saying 'sorry'", loud banging, and a man screaming about the loss of a shoe, jurors were told.
Prosecutors say the banging could have been from "repeated assaults" on Alex in the Mountsfield Park in Catford, south-east London.
Iheanacho, from Hounslow, west London, is standing trial at Woolwich Crown Court, where he denies murdering the boy.
"The prosecution say that he died at the hands of this defendant, a man who was looking after him, acting as his stepfather, but who on the afternoon/early evening of November 20 last year, lost his temper and violently assaulted the boy, causing him fatal head and stomach injures," said prosecutor Eleanor Laws QC
"The defendant is a man who has ever since, we say, done his best to avoid being held accountable for those injuries."
A jury of seven men and five women heard he was in a relationship with Alex's mother Lilya Breha and would often stay at her flat in Catford.
CCTV captured Iheanacho taking Alex from his home, on three separate buses, to the park, where they arrived at around 5.12pm, when it was already dark.
Alex was wearing black trainers, a red jacket, a woolly hat and gloves.
Ms Laws told jurors there are no witnesses or CCTV footage of "the defendant landing blows on Alex", but continued: "There is, however, clear evidence as to the fact the defendant lost his temper with Alex before he sustained his injuries."
She said prosecutors know the pair went to the play area because Alex lost one of his trainers, which was later found there by police.
Describing an incident at about 6pm, she added: "The defendant was heard shouting loudly at Alex after finding out that Alex had lost his shoe."
One witness, Sarah Strugnell, allegedly saw Iheanacho bend down to the child and ask where his shoes were.
"The man was very angry indeed and Sarah Strugnell describes how he was raging at the child who was very quiet," said the prosecutor.
"Her partner recalls hearing the loud banging and a male voice screaming about the loss of shoes and a child's fearful voice saying 'sorry'.
"He describes the banging continuing. He shouted to his dogs which appeared to bring the male's shouting to an end.
"It is the prosecution case that this banging could well have been in fact banging from repeated assaults upon Alex.
"At some point, whether during this confrontation or between this confrontation and the next sighting of the defendant by dog-walkers, soon after, back in the park, the boy had received extreme injuries."
Judge Mark Dennis QC told jurors the main issue in the case is how Alex sustained those injuries and said the trial will last between two and three weeks.
The court heard Iheanacho carried Alex unconscious "as if he were a baby" to a minicab office, from where he was taken back to Ms Breha's flat at about 7pm, while the nearest hospital was just a five-minute walk away.
He told Alex's mother her son fell to his knees and hit his head and that he slapped him to try to wake him up, jurors heard.
Ms Laws said Iheanacho attacked a screaming Ms Breha after she called him a "danger to her family" and stopped her from calling an ambulance.
But she grabbed the phone after noticing her son was getting cold, his face had turned blue and he had stopped breathing.
The court heard Iheanacho told one paramedic Alex had fallen onto his knees and hit his head on the floor, but told others he had fallen from a climbing frame.
Doctors at Lewisham Hospital tried to resuscitate Alex, but a CT scan revealed he was suffering from severe brain swelling, and he was transferred to King's College Hospital.
But an operation was unsuccessful and he was pronounced dead at 3.19pm on November 22 last year.
A post-mortem revealed bruises on Alex's head, neck, and body, while a pathologist concluded the combination of impact type head injury and blunt trauma to the abdomen was "consistent with inflicted injury".
The prosecutor said Iheanacho denies causing any of the injuries to Alex, describing what happened as "an accident".
But she said Iheanacho delivered a "forceful blow", such as "a kick, a stamp, or a punch," and added: "The prosecution say that Alex's death was no accident.
"The injuries suffered were extensive and did not result from a fall.
"The defendant lost his temper, most likely because Alex had lost his trainer.
"His previous convictions demonstrate that he had a temper.
"He has previous convictions for violence and has a tendency to lose his temper and lash out."