But he also insisted May’s Holyrood election could be part of an “absolutely seismic moment” where, for the first time, the leaders of all the devolved nations in the UK could be “committed to independence from the UK”.
Mr Swinney said there “could be no clearer sign” that “Westminster’s time is up”.
There is a Sinn Fein first minister in Northern Ireland, and in May’s Scottish and Welsh elections, there could be victories for the SNP and Plaid Cymru, marking the first time in devolution that all three leaders have come from pro-independence parties.
In his keynote speech, he said: “We are closer to becoming independent than we have ever been. We can almost touch it.
“Support for our cause has never been at such sustained high levels.”
Mr Swinney needs his party to achieve a majority of at least 65 seats to trigger a second independence referendum.
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That was last achieved by former leader Alex Salmond in 2011, with a referendum taking place in 2014.
Mr Swinney said his party now “need to do the same again”.
It came as Mr Swinney set out to win the votes of working parents with a “transformational” extension of free childcare.
Polling suggests the SNP will be re-elected, while Labour and Reform UK will be fighting for second place.
If that happens, childcare support would be made available for every child in the country, from nine months old through to the end of primary school, by the end of the next parliamentary term.
This help would be available to parents 52 weeks a year, Mr Swinney pledged, and would be “backed by over £0.5 billion of new investment”.
The announcement comes after, in its 2021 election manifesto, the SNP had promised to build a “system of ‘wraparound’ childcare – providing care before and after school, all year round”.
SNP sources, however, pointed to the funding linked to Saturday’s commitment from the First Minister, who promised: “We will deliver a brand-new, childcare system that fits around families – rather than expecting families to fit around the system.
“And because parents’ work doesn’t stop during the summer holidays, neither will the provision of childcare.”
While some families will have to pay some costs, for those most in need childcare could be entirely free.
“Our new approach will mean families benefit from between £1,400 up to over £11,000 dependent on need,” Mr Swinney said.
“Every single family in Scotland will get help.”
He also promised a re-elected SNP government would “step up” to help those who are struggling to buy a home of their own.
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Speaking about how many young people “don’t believe that owning their own home will ever be a reality for them”, Mr Swinney said his Government would look to help those who had been “locked out of home ownership”.
He announced to the conference: “If re-elected, we will provide up to £10,000 towards a deposit to give people the help they need to buy their first home.”
In another pre-election promise, he said the SNP would also seek to double the number of walk-in GP clinics.
In October last year, the First Minister set out plans to create 15 such clinics, but he has now promised if his party wins the May election it would deliver 30 such facilities.
Scottish Conservative leader Russell Findlay MSP said: “John Swinney’s speech was a stark reminder of what is at stake at the election in May.
“He has made it clear that every vote for the SNP will be presented as a mandate for another divisive independence referendum.
“He has already said that he will deploy tactics to break up the United Kingdom. And that’s the risk of an SNP majority.”
