Police this week produced up to 530 hours of material on cassette tapes, taken from listening devices planted in Folbigg's home.
The box of tapes was discovered after extensive searches that started last year. It is not clear whether they contain any relevant material.
The head of the inquiry, former NSW chief justice Tom Bathurst KC, expressed concerns about the timing.
"It is a matter of real concern that they were only produced so late," he said.
"I don't want Ms Folbigg waiting a considerable amount of time for my report."
Mr Bathurst also raised the prospect of the inquiry proceeding in the knowledge "there's something there that might reveal something".
The inquiry finished hearing evidence on Friday ahead of closing submissions in April.
Prosecutors acknowledged the late production of the tapes was a problem but said it was "very unlikely" they contained anything relevant.
Folbigg is serving a 25-year minimum sentence after being found guilty of three counts of murder and one of manslaughter in 2003.
She maintains her innocence and claims her four babies - Laura, Sarah, Caleb and Patrick - all died of natural causes between 1989 and 1999.
Folbigg and her two daughters were later found to carry a rare genetic variant, casting doubt on her convictions and triggering the inquiry, which is the second of its kind.
A number of witnesses gave evidence on Friday, including Yumna Dhansay, who was questioned about Folbigg's diaries.
Dr Dhansay said it was noteworthy the diaries were silent on one crucial question: "Why are my children dying?"
"Maybe it's because she's so avoidant that she doesn't want to go there as it's too painful," the psychiatrist said.
The diaries also contained no admissions of guilt.
"I would have thought that if she was guilty there would have been something more implicating," Dr Dhansay said.
"There's nothing like that there."
Dr Dhansay was also asked about Folbigg hiding the diaries, saying the conduct could be interpreted to reflect "consciousness of guilt" in relation to the deaths of her children.
Barrister Dean Jordan SC, appearing for the NSW Director of Public Prosecutions, drew attention to a diary excerpt saying Folbigg's daughter Sarah left "with a bit of help".
Dr Dhansay said she took the phrase to refer to a "higher power".
Mr Jordan said an alternative explanation was Folbigg was saying: "Sarah left with a bit of help, by Ms Folbigg".
"Yes, I do accept that's an alternative explanation," Dr Dhansay replied.
The inquiry also heard from Stephen Cordner, who authored a report which concluded there was nothing from a forensic pathology perspective to suggest the children had been killed.
Professor Cordner was questioned about the statistics underpinning his review of smothering cases.
He was asked whether his conclusions were skewed by "selection bias" due to the omission of smotherings not established as intentional.
He stood by the work, saying of the methodology: "If they're not established to be intentional, then we can't say they're intentional smothering".
"What we're trying to get to in this matter, I believe, is whether or not the four Folbigg children can be said to have been intentionally smothered."
The inquest resumes on April 26.
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