In a video recording released by police, the parents of Gus, Josh Lamont and Jess Murray, made an emotional plea for help to find their son, who has been missing for almost 12 months.
Ms Murray said the little boy's disappearance had been the "most devastating and inexplicable event we have ever experienced''.
''We love him more than words can convey and every single day without him has been incredibly difficult,'' she said.
''Our heartache only grows as time passes and an entire year without any answers is upon us.
''Our memories of Gus are of a beautiful, sweet and unique little boy who loved music, listening to stories and playing in the natural world.''
South Australian Premier Peter Malinauskas announced on Wednesday the government was matching the highest reward in the state's history for information leading to a body or a criminal conviction.
"Justice needs to be done in one way or another,'' Mr Malinauskas said.
"We will not tolerate, as a state, any circumstances where children go missing are not able to be accounted for.
"We throw everything at it."
Detectives have previously said Gus was last seen by his grandmother playing on a mound of dirt near the homestead at Oak Park, a sprawling sheep station near Yunta in outback SA, on September 27, 2025.
Josh Lamont said the love and support from family and friends had been overwhelming, keeping them strong and hopeful for the future.
''We miss Gus more than we can describe, we are desperate to have him return home to us, and we are desperate for answers,'' he said.
''Someone knows what happened to Gus and may even know where he is.''
The focus of Task Force Horizon remained on the theory someone known to Gus was involved in his disappearance and suspected death, Detective Superintendent Darren Fielke said.
"I've previously stated that one of the grandparents is a suspect in our investigation," he said.
"That has not changed, but I'm not going today to make any more comment or elaborate any further about the suspect."
The only other people at the property at the time were Gus's grandmother Josie Murray, his mother, and the boy's younger brother.
In February, police said they had identified ''inconsistencies and discrepancies'' in timelines provided by family members and a person living at Oak Park had withdrawn their support and was no longer co-operating with detectives.
In an interview this week, Gus's grandmother Josie Murray said it ''brings me to tears that he's not here''.
Ms Murray said she wanted to know what happened to her grandson.
Police had told her she was the main suspect but she believed Gus was taken by a stranger.
''I think he has to have been taken,'' she said.
''Nothing else makes sense.''
Det Supt Fielke said detectives were "working their asses off on this job".
He announced on February 5 the incident had been declared a major crime and police believed Gus was no longer alive.
On Wednesday, he said there had been 11 ground searches over the past year covering more than 700 square kilometres, involving hundreds of personnel.
''No stone has been left unturned in relation to our search efforts,'' he said.
Recently, Task Force Horizon detectives had completed a painstaking manual search of aerial imagery, in addition to AI analysis.
''We have identified some anomalies in the imagery ... these are now being further reviewed and ... will determine whether we return to Oak Park Station and conduct further searching,'' Det Supt Fielke said.
