The inquiry will spend three months evidence-gathering in private
The Disclosures Tribunal is urging potential witnesses or those with information to come forward urgently.
Mr Justice Peter Charleton has made the plea as he delivered an opening statement in public for the inquiry that is examining if there was an alleged smear campaign against garda whistleblower, Sergeant Maurice McCabe.
He warned potential witnesses that if they tell lies, do not cooperate or hinder the work of the tribunal, they are wasting taxpayers' money.
Mr Justice Charleton has appealed for written submissions from possible witnesses within the next two weeks.
“Are you a witness to this matter? Then the tribunal needs your help, and needs it urgently.
“Many have already indicated publicly, and in various circumstances, that they have some knowledge.
“Now the opportunity has arrived to cooperate with this tribunal”.
The inquiry will focus initially on the allegation that senior officers in the force participated in a smear campaign to discredit Sergeant McCabe.
It will also examine the circumstances of the Tusla file created about Sergeant McCabe, which included a false allegation of sex abuse.
The treatment of other Garda whistleblowers will be looked at later in the inquiry.
Although a smaller-scale Commission of Investigation was originally planned, earlier this month it was changed to a full public inquiry amid public and political outrage over the allegations.
Earlier, Mr Justice Charleton said he hoped there would be no need for anyone to go to the courts looking for a judicial review of his inquiry.
The opening - which comes less than a fortnight after the terms of reference were agreed - was largely ceremonial.
Speaking at Dublin Castle, Mr Justice Charleton noted that we have already seen 'several tribunals'.
"The basic touchstone is fairness and balance of application of procedures," he said. "There should be no need for further judicial reviews."
It is claimed that Garda Commissioner Nóirín O'Sullivan told her lawyers to question Maurice McCabe's motives at a previous Commission of Investigation.
Mr Justice Charleton also said it is not clear exactly whether Commissioner O'Sullivan can be forced to give evidence about her instructions.
He also questioned if the media was used for "naked deceit".
He said he wants to complete the work speedily and establish the truth, saying: "This tribunal is a drain on the resources of the Irish people. Every lie told to this tribunal will be a waste of what ordinary men and women have paid for."
In a break with tradition, the session was also open to TV cameras.
After today, the inquiry will now gather evidence in private before public hearings commence.
Professor Shane Kilcommins, Head of School of Law at University of Limerick, says there is also speculation that those hearings will be televised.
Talking to Newstalk Breakfast earlier, he explained: "It's only at the fourth stage [of a tribunal] that it will become public - whereby witnesses in questions will be examined [...] and then cross-examined.
"Whether it's a good thing or a bad thing, I would say that Mr Justice Peter Charleton has decided that he is going to broadcast - because the issue itself is of such public important that ensuring it's as transparent as possible can be done by conducting this via TV."