That was when children were experiencing "the most persistent poverty" at that time, she said.
Families with newborn babies would be $60 better off a week, she said.
All families will receive the payment in their baby's first year. For families receiving Paid Parental Leave, the Best Start payments would begin after those ended.
"It's really an acknowledgement about that being such an important period," Ardern said.
Best Start was tested with a lot of people and it "stood the test of time".
"I think the principle behind it is really, really solid."
As part of the Working for Families changes the Governement is increasing the Family Tax Credit base rate for the eldest child and for subsequent children, she said.
Essentially everyone who was receiving the Working for Families would receive more, Ardern said.
Anyone currently receiving NZ Super or a benefit would receive the winter energy payment, she said.
Those payments would be $450 for a single person and $700 for a couple or a family.
The Families Package, which was funded by cancelling the previous National government's planned tax cuts, will cost $5.53 billion over five years.
The Government estimates that by 2020/21, when the package is fully rolled out, some 384,000 families with children will be better off by about $75 a week. It is projected to lift the number of children living out of poverty by 64,000, or about 41 per cent, by 2020.
Families Package measures which take effect on July 1 include:
• An increase in paid parental leave from 18 to 22 weeks, and a further increase to 26 weeks on July 1, 2020
• A rise in the Family Tax Credit and Working for Families abatement threshold, making 26,000 more families eligible, rising to 39,000 by 2020/2021
• An automatic winter energy payment for beneficiaries, superannuitants and veterans' pension beneficiaries. Those who don't want it can opt out
• An increase in the orphan's benefit, unsupported child benefit and foster care allowance by $20.31 a week.
• Increases in accommodation supplement and benefits, announced by the previous National government.