Mr Minns used his budget reply speech on Thursday to begin differentiating his party from the Liberal-National coalition that has governed NSW since 2011.
He called for a serious and constructive debate about the state's future in the lead up to the March 2023 election.
"Our people face a future of deep uncertainty, of spiralling costs, of slow wage growth – and an ever-growing sense that our economy demands of the many, but only delivers for the few," Mr Minns said.
He said a Labor budget would have provided more help for household budgets, invested more in education and shaped the economy to deliver more for more people.
Treasurer Matt Kean on Tuesday laid out his "10-year blueprint for prosperity", containing quarterly toll road rebates, back-to-school vouchers for parents and subsidies for preschool among other cost-of-living measures, and more wide-ranging policies Mr Kean said focused on reform.
Mr Minns said Labor would go further on toll relief, using revenue from the toll roads the state still owns to subsidise the cost for drivers on the ones it no longer does.
He promised to keep the Sydney Harbour Bridge and Tunnel in government hands, and after his speech said it would be a gross breach of trust for the government to privatise the assets in the months between contracts expiring in August and the election in March.
Opposition education spokeswoman Prue Car said Labor's plans to build 100 preschools at new and existing primary schools and under-served areas in its first term was more proactive than the government's long-term plan for a universal year of pre-kindergarten by 2030, much of the funding for which is beyond the forward estimates of Tuesday's budget.
But Labor's eventual education policies at the election will need to address staffing.
"We will need a comprehensive teacher recruitment strategy," Ms Car said.
"(The government) have failed on every single account to recruit enough teachers."
Opposition treasury spokesman Daniel Mookhey has already begun looking for ways to pay for Labor's promises to do more than the government.
"The Transport Asset Holding Entity (TAHE) goes - that entity will burn a $13 billion hole in the NSW budget by 2031," Mr Mookhey said.
Labor's campaign will likely attempt to tie TAHE closely to Premier Dominic Perrottet, who established it.
The state-owned corporation controls transport assets and charges operators such as Sydney Trains for access.
Labor has long called TAHE a budget con and part of a larger plan to privatise public transport.
Local manufacturing and procurement will be another focus as Labor seeks to return to government after being out of power since 2011.
The party has criticised the government's procurement policies in recent months, particularly in relation to transport.
NSW is still waiting for cracked Spanish-built trams to return to service, and the continued use of new ferries built in China are under review.
Mr Minns wants to restore the "proud history of building in NSW" and it would be his first priority if elected.
Labor will set a target of 50 per cent minimum local content for rolling stock contracts and increase tender weightings to 30 per cent local content.
The NSW Jobs First Commission would also be established as an independent body to oversee local industry growth and advocate for businesses bidding for government contracts.