Epidemiologist Dr Charles Alpren told the inquiry an "episode of environmental contamination" took place in the family's room on May 18, which nursing staff needed to address.
It is thought the family's distressed children spread human waste in the room.
"Subsequently there is a suggestion that the family were approved to walk outside their room, during which they were accompanied by security guards," Dr Alpren said.
"It is possible a transmission event or events happened at this point."
More details about the conditions inside Melbourne's quarantine hotels will be revealed when security guards, returned travellers and officials give evidence at the inquiry chaired by retired judge Jennifer Coate.
Two nurses and four returned travellers will give evidence on Thursday, and another two travellers and a security guard will front the inquiry on Friday.
Meanwhile, in his national update earlier yesterday, Prof Michael Kidd urged Australians to not neglect any other health issues for fear of being exposed to Covid-19.
The Deputy Chief Medical Officer said he was "very concerned" to hear some people were delaying treatments and appointments because they didn't want to come in contact with the virus in healthcare settings.
"While much of our focus remains on Covid-19, it is absolutely essential that we continue to focus on all our healthcare issues that affect the people of Australia," he said.
"Our Australian attitude of 'she'll be right' doesn't apply to your health or the health of your loved ones."
