Bulldozing by police began early on Sunday morning in the Royal National Park south of Sydney, clearing out dense bushland and dirt just metres from the main road.

Matthew vanished in September 2007 after a night out at Sydney's ARQ nightclub with his then-boyfriend Michael Atkins, who was charged and later acquitted of his murder two years later.

Mark Leveson, father of the 20-year-old missing man, was "quiet and hopeful" that police will find evidence of his son's body.

"The police are searching with patterns to make sure they miss nothing. So it's long and slow but in doing that, they're not missing a square centimetre," he said.

Matthew's mother, Faye Leveson, hoped that a recovery of the body would bring closure to the family.

"It's been a long, long nine years and we just want to bring him home," she said.

"I just want to be able to lay him to rest and for his brothers to know where he is now."

On Saturday, an undisclosed item was retrieved by police as evidence for further analysis.

In a surprise breakthrough last Thursday, Mr Atkins broke years of silence to lead police to Matthew's possible burial site after striking an immunity deal with NSW Attorney-General Gabrielle Upton.

The deal means he cannot be prosecuted for perjury or contempt of court arising out of the evidence he gave before the coronial inquest last week. It adds another layer of protection to that already granted to Mr Atkins by the Coroner's Court, whereby his evidence cannot be used against him in a future trial in connection with Mr Leveson's death.

In the nine years preceeding Matthew's disappearance, the Levesons scoured the Royal National Park day and night, going as far as "thinking like a killer" in a bid to find Matthew's body.

The search continues on Monday.

Correction: The original version of this story said the immunity clause means that Mr Atkins cannot be prosecuted for any evidence he gives on Matthew's death, unless he commits perjury or contempt of court.