The centrepiece government policy, announced on the weekend, promises to deliver as much as $49,000 on a child's 18th birthday towards their education and housing.
All kids 10 and under would get an account, with the government tipping in up to $400 a year.
Before boarding his all-electric, Australian-made campaign bus for the first time on Monday, Mr Minns rejected the "very expensive" policy for failing to address 'here and now' problems, such as chronic underfunding of public schools.
"(Parents) know we need to turn around the education system so if there's fair resourcing from the NSW government, it's got to go into education," he told reporters from the key western Sydney seat of Riverstone.
"That's the best gift we can give to future generations of young Australians."
He questioned what benefit the accounts provided to low and middle income families with multiple children, already face rising expenses.
"I'm just asking everyone to think about the hard-working families on an average income in NSW, both mum and dad work and they don't have a spare two or three thousand (dollars) to put into that account," he said.
Premier Dominic Perrottet, also campaigning in Riverstone, rejected the idea the coalition couldn't provide relief from rising living costs now and set aside $850 million over the next four years for the state's youngest residents.
"We're doing both," he told reporters.
"We have a $250 rebate on energy bills that will be scrapped by Labor, we have our back-to-school vouchers, active kids vouchers ... over $7 billion in cost-of-living relief, more than any other state in this country."
The kids future fund had been a long-held passion for the premier but had stayed on the back burner as he tried to overhaul his bugbear, stamp duty.
He took advice from unnamed experts and looked to overseas schemes, such as Canada's education savings grant scheme.
Under the blueprint, each child's fund would be fee-free and could receive up to $1000 a year from parents and grandparents, with the first $400 matched dollar-for-dollar by government.
The interest rate would match the state's sovereign wealth fund, aiming for yearly returns of seven per cent.
Poorer children would receive top-ups without co-contributions, taking their accounts to about $8100 over 18 years, while maximum contributions would deliver as much as $49,000 at adulthood.
"This supports every mum and dad - every child in NSW is so much better off with this approach," the premier said.
Fund earnings would be liable to income tax but withdrawals could occur over many years, potentially lowering the tax burden, the government said.
Federal Nationals leader David Littleproud was asked about the policy but didn't provide his full support, telling Sky News he wasn't across the detail and thought housing supply was a key issue entering the market.
Meanwhile, Labor has committed $560 million in road upgrades for Sydney's northwest, which is expected to grow to about 90,000 households and 250,000 residents once fully developed.
