Australia

As someone with a three year old kid in Australia, I think the government does a pretty good job at all of those things.

For example we've only ever paid medical bills for things that were totally optional, and the free services were extensive (including repeated 1:1 home visits by a professional midwife - for free, and for the actual birth there was more staff attending that mum than anyone else in the hospital gets - even Intensive Care Unit patients get a lower level of care).

Education will be free starting next year, and the optional education he's enrolled in this year and in the last couple years have been extensively subsidised (and would be subsidised even more if our income was lower).

Money and time are and always will be in direct opposition to each other and every parent has to make a tradeoff between the two, and not really anything the government can control. But it's worth noting basic living expenses (like staple foods) are largely exempt from taxes, and the recent high cost of electricity, due to the ukraine war, has triggered government assistance packages to help people out (everyone, but low income people have been get even more help — we actually haven't paid an electricity bill at all the last 8 months or so - from memory we're about $100 in credit due to various subsidies).

Could it be better? Sure - for example I think free education should start younger and include things like swimming lessons (enough to not drown). But I don't really have any complaints.