Hank Shannon Sherriff, 25, was arrested and charged on February 2 with murdering his infant son.
Investigators allege the baby was injured at a home in Greenbank in Logan, south of Brisbane, in July before relatives took him to hospital.
Sherriff, who has been in custody since his arrest, was not required to appear in person when his case was mentioned on Wednesday at Beenleigh Magistrates Court.
His solicitor asked acting magistrate Sarah Thompson for an order for police to produce a full brief of evidence by a certain date.
Police prosecutor Sergeant Duncan Erskine said he had been given a note by the arresting officer in Sherriff's case.
"The arresting officer has requested the indulgence of the court for the more than usual time to prepare the brief of evidence," Sgt Erskine said.
"Is there something complicated about it?" Ms Thompson said.
"There is going to be what I suspect to be extensive medical evidence based on the myriad of injuries that are listed in the (charge sheet and alleged facts) and the other agencies the officer seems to have been liaising with", Sgt Erskine said.
The boy died in Queensland Children's Hospital on July 22, 2024 from internal injuries, police said.
Family members had taken him there in a serious condition but with no obvious injuries.
"Sadly and unfortunately, that three-week-old child passed away four days later," Detective Acting Inspector Glen Antonie told media earlier in February.
The boy's death triggered a lengthy police investigation named Operation Whiskey Nell.
Detectives alleged the boy sustained internal injuries.
On February 4, a 24-year-old Southport woman was charged with one count of cruelty to children under 16 years in relation to the boy's death.
She is due to appear at Beenleigh Magistrates Court on March 4.
Ms Thompson ordered a full brief of evidence to be disclosed to Sherriff's legal defence by April 7.
Sherriff was remanded in custody for his case to be mentioned again in court on April 21.
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