The inquest into the death in 2015 started on Monday and is examining if police could have prevented Mr Cheng's death and that of the 15-year-old shooter Farhad Khalil Mohammad Jabar.
The year 10 student was shot dead by a special constable at police headquarters in Parramatta in Sydney's west, moments after executing the 58-year-old Mr Cheng on October 2, 2015.
"A hard-working father and member of the community on the way home to his family after a hard day of work apparently killed by someone so young tragically under the sway of a violent extremist ideology," counsel assisting Rob Ranken SC said during his opening address.
Mr Cheng's widow Selina Cheng, and his children Zilvia and Alpha wore black as they sat in the court's public gallery.
From the witness box, former Detective Chief Inspector Mark Henney said police officers from the NSW Joint Counter Terrorism Team could not have taken any further steps to prevent the tragedy.
Two special constables who confronted Farhat in the lethal showdown were found to have acted appropriately, the court heard.
Four men, Raban Alou, Milad Atai, Mustafa Dirani and Talal Alameddine, have been sentenced for roles providing a revolver to Farhat.
On Monday, Mr Henney said the 15-year-old had gone to a gathering with a number of individuals including Alou and Atai at Lake Parramatta Park on September 11, 2015.
At the time, officers did not know who he was and were targeting others at the meeting, Mr Henney said.
Alou and Atai were under police surveillance as part of a terrorist group allegedly planning an attack at another Sydney location.
Alou, Atai and Dirani sourced the firearm from Alameddine.
Alou is believed to have given the gun to Farhat in a CCTV black spot at a Parramatta mosque an hour before the attack.
The inquest, which comes more than a decade after the shooting, had to wait until the various criminal cases against the four men concluded.
Alpha Cheng told reporters on Monday there were two tragedies from the attack.
"One for ourselves and the family losing dad in such a way," he said.
"But also the tragedy of someone who's 15 years old being involved and radicalised and having the ability to do such an act of terrorism."
Deputy State Coroner Derek Lee has been asked to look at police actions on the day as well as steps officers could have taken to intercept Farhat and others before the shooting.
The coroner has also been asked to look at how police and the community can tackle radicalisation.
It was only after the shooting officers realised Farhat and his sister Shadi Jabar had been accessing extremist material online, Mr Henney said.
He told the inquest police would not have suspected the siblings.
Their family were Kurdish and deemed unlikely to support Islamic State, he said.
Ms Jabar left Australia for Turkey the day before her brother was killed.
She travelled to Syria to assist Islamic State fighters and it was believed she had been killed by an air strike in 2016, Mr Ranken said on Monday.
Farhad's older brother Farshad Jabar reported them missing to police with the family being unaware of their intentions, he told the court.
The inquest continues on April 28.
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