A majority of voters would not mind if Australia Day was shifted to a different date and most don't know why it's currently held on January 26.
New polling also reveals that only about a third of Australians - 37 per cent - realise the date is offensive to many Indigenous people because it represents the beginning of the dispossession and violence of British colonisation.
As the political and community debate about the "change the date" movement continues to intensify, the Research Now survey of 1417 people suggests nearly all Australians - 84 per cent - think it is important the country has a national day of celebration.
But 56 per cent say they don't mind when the day occurs, challenging the notion that Australians see January 26 as sacred or untouchable.
The polling also reveals 77 per cent of people believe - incorrectly - that the celebration has always occurred on January 26, the date the First Fleet planted the flag in NSW in 1788.
The date was in fact not adopted by all states until 1935, and has only been celebrated in its current form since 1994.
The polling commissioned by the progressive Australia Institute think tank was conducted among a nationally representative sample in December.
"This polling shows that while Australia Day is important to most Australians, most people are laid back about the date we celebrate on," said deputy director Ebony Bennett.
Given 11 multiple choice options, 38 per cent correctly identified the event January 26 marks. And just under half knew it had anything to do with the First Fleet at all.
Others believed it marked the day Captain Cook first sighted Australia, the day the constitution was signed or the day Australia became independent.
Four per cent of people linked the date to events that have not actually happened, including becoming a republic or signing a treaty with Aboriginal Australia.
Asked to nominate what date would be the best to celebrate Australia Day, 70 per cent preferred a date not associated with the First Fleet. And fewer than a quarter (23 per cent) selected the landing in Sydney Cove as the best of a range of options.
Only 37 per cent of people agreed the current date was offensive to Indigenous people, even though many Indigenous leaders have long been calling for change. Nearly half of people - 46 per cent - disagreed the date was problematic.
Asked if Australia Day should not be on a day that is hurtful to Aboriginal people, 49 per cent agreed and 36 per cent disagreed.
The polling came as Indigenous Labor MP Linda Burney said January 26 was "extremely painful" for many first Australians and represented "an attack on sovereignty" - although Labor does not support a change to the date.
Ms Burney wants a renewed focus on constitutional recognition and is advocating for a national public holiday to recognise first Australians.
She also criticised the increasing "jingoism" creeping into Australia Day.
"I don't think it makes you any more Australian if you wrap a flag around you and tattoo the Southern Cross on your neck," she told ABC radio.
But Ms Burney - a shadow minister and the first Indigenous woman elected to Federal Parliament's lower house - also criticised the Greens, saying its new campaign to change the date "could end up being more divisive than helpful".
This year's Australia Day debate kicked off in earnest earlier this week after Greens leader Richard Di Natale announced a new campaign for change, signalling it would be one of his party's top priorities in 2018.
Prime Minister Malcolm Turnbull said the Greens had become "a parody of themselves".
"Australia Day is a day on which the overwhelming majority of Australians - all but a handful - are proud of Australia and its achievements," he told 2GB radio.