Labor took at least nine seats from the government in Saturday's contest with a statewide two-party preferred swing of seven per cent.
The result also spelled the end of outgoing premier Dominic Perrottet's leadership of the Liberals, with his deputy Matt Kean later also standing aside, citing family.
Even before his swearing-in as the state's 47th premier, Mr Minns was on the front foot on Sunday, making his first direction before noon.
"No, you're not getting a flat white," he told 12-year-old son Nicholas as the Minns family, surrounded by photographers, ordered drinks at a Kogarah cafe.
Later, in his first press conference, he committed to working for all, "whether you voted Liberal, National, Labor or for a minor party".
"We will make sure you've got a government in place you can be proud of and that will work on behalf of the people of NSW," he said.
Mr Minns noted there was not a moment to lose and sat down with his leadership group on Sunday afternoon to map out his government's initial steps, including removing the public sector wages cap.
While the timing of their swearing-in is up in the air, Ryan Park (health), deputy leader Prue Car (education), Jo Haylen (transport) and Penny Sharpe (environment) will stick with the portfolios they held in shadow cabinet.
That would "largely" be the case for the first Minns ministry, though its exact formation will come after individual seat counts are clearer.
One man asking for a portfolio could be former primary industries and emergency services minister Steve Whan, who mounted a 15 per cent swing to rip bellwether Monaro from Nationals hands.
"I'll have those conversations with my colleagues in the next few days," Mr Minns said.
Labor is predicted to form a comfortable majority, after claiming Parramatta, East Hills, Heathcote and Riverstone in Sydney's south and west, and regional seats including South Coast.
The Liberals have conceded retiring health minister Brad Hazzard's former seat of Wakehurst, after an independent challenge by local mayor Michael Regan.
Penrith, Camden and Terrigal also appear to have fallen, though the Liberals are hoping pre-poll and postal votes can turn the tide.
"Apart from obviously asking for an unprecedented 16 years, the retirement of hard-working local members made a considerable difference," a NSW Liberal Party spokesman said.
The ALP now governs every mainland state and territory, with Tasmania the last Liberal holdout.
"It shows just like we have at a federal level, we've sort of got that approach which brings people together on many of the big challenges facing our state and our country," Federal Climate Change Minister Chris Bowen told ABC Radio on Sunday.
Federal Liberal Andrew Bragg and Perrottet minister Alister Henskens were out early on Sunday trying to lift party morale, pointing to success in holding electorates in the inner suburbs and North Shore and urging against a shift to the right.
Labor ending up with 45 to 48 seats, in a parliament requiring 47 votes for a majority, would make for a very narrow parliament and a "hotly contested political environment", Mr Henskens told Sky News.
He dodged a question about his own potential tilt at the leadership, while not ruling himself out.
Outgoing treasurer Mr Kean did put a line through himself, choosing to "hang out and be a dad" to three-year-old Tommy while serving his Hornsby electorate.
"I have a young family and I would love to spend a little more time with them," he said late on Sunday.
"The election result will enable me to do that."
