"It amazes me that we've had no documents whatsoever," Britain's 11-times Paralympic champion Tanni Grey-Thompson, one of the three members on the commission, told International Cycling Union counsel Ian Mill.
Mill also told the hearing that a date for a commission hearing set provisionally for April 9-26 would need to be rescheduled.
Friday's hearing was intended to set up the procedures, fix a timetable and set a date for a hearing. However, it hit immediate stumbling blocks and was adjourned to January 31.
Mill said there had been "no desire to suppress or conceal any documents", with 16 files of material available, but cast doubt on the commission's need for them, with the possibility of a broader 'truth and reconciliation' hearing being set up with other bodies.
In increasingly testy exchanges between the commission members and the UCI lawyer, it was made clear that the process could take up to two years, if the commission were not suspended entirely.
Mill said it was clear in any case that it would not be possible for the proposed April hearing to go ahead and a report would not be ready for June.
Responding to concern expressed by the independent commission chair Philip Otton, who had expressed a fear that allegations against the UCI risked being "kicked into the long grass", Mill said: "We're not trying to kill this enquiry, we set you up."
"Now you want to knock us down," said Otton, before withdrawing the comment.
After a 45-minute break, Otton told the hearing that the UCI had agreed to make documents available to the Commission and the hearing was adjourning "with considerable reluctance". Next week's hearing will decide how to proceed.
"On that occasion, we will consider whether or not the Commission will continue on the present timetable," he said.
Otton said it was "blindingly obvious" that there was immense public interest in determining why and how Armstrong's US Postal Service team was able to engage in systematic doping without detection or sanction.
Armstrong has been stripped of his seven Tour de France titles after a USADA report, that included testimony from former team-mates, revealed what it called "the most sophisticated, professionalised and successful doping programme that sport has ever seen."
The UCI, who dope tested Armstrong 218 times without a positive result, set up its independent commission to investigate allegations made against it in the affair.
Mill said the UCI was open to a truth and reconciliation process, with the world anti-doping agency WADA and the US anti-doping agency USADA, but subject to changes to the WADA code to allow an amnesty to be offered to those testifying.
"The UCI has accepted that a truth and reconciliation process was one they wish to engage with, notwithstanding that it was limited to the problems of doping in the sport of cycling," he said.
"WADA has accepted that its code would require to be changed so as to enable the sort of amnesty to be offered which would be likely to result in important evidence being made available.
"We have asked WADA to tell us how and when such a change to the code can be achieved."
Mill said the independent commission appeared to envisage such a truth and reconciliation process forming part of their enquiry, but that might not be the case.
"That was not what this (independent) enquiry was designed to do," he said, pointing out that the UCI had spent a considerable sum on the commission and funding another longer and broader one was beyond the resources of the UCI alone.
"If others, in particular WADA, are being asked for help to fund the process then they have to have the opportunity to discuss and agree with us the process itself and we envisage that," added the lawyer.
"It therefore does not follow that this commission will ultimately be involved in that process."