The commission is investigating how schools, churches and government bodies responded to abuse claims and cases.
It has also called for a national system for checking the history of people who seek to work with children.
The commission was formed in April 2013, following pressure from lawmakers amid police claims that the Roman Catholic Church had concealed evidence of paedophile priests.
There were revelations that child abusers were being moved from place to place instead of having their crimes reported and investigated. There were also accusations that adults had failed to stop further acts of abuse.
On Friday, the commission's chair, Justice Peter McClellan, called for responses to the consultation paper so that a final report could be published in the middle of this year.
"It is necessary for me to stress that the commissioners do not presently have firm views about any issue in the consultation paper," said Mr McClellan.
Actuaries estimated 65,000 victims may be entitled to some level of redress, with an average payment of A$65,000.
"Based on these assumptions, the total cost of redress nationally would be in the order of A$4.378bn," Justice McClellan said.
In the two years since the commission was appointed, its commissioners have spoken to more than 2,850 survivors of child abuse in private sessions. It has also completed 21 public hearings and expects to hold another 17 hearings this year.
'Blight upon communities'Justice McClellan said the commissioners were developing a picture of a period when thousands of children were abused in a "high-risk environment", created by "prevailing social attitudes to children and unquestioning respect for the authority of institutions by adults".
However, he acknowledged that the abuse of children "is not confined in time - it is happening today".
Justice McClellan said there had long been a need for a national framework to check the backgrounds of people working with children.
"Its absence is a blight upon the communities' efforts to provide effectively for the protection of children," he said.
The consultation paper said the compensation scheme would be funded by contributions from both governments and institutions.
If the state was a funder of last resort, a contribution of almost A$2bn would be required from various government authorities, and A$2.4bn would come from private institutions.
The commission expects to provide a final report by December 2017.