As others have noted, having good taxpayer funded parental leave increases labor force participation by women, and makes parents more effective workers by reducing stress and increasing employee flexibility. The spending would go into the current network of small providers allowing many peope to start and run businesses that currently struggle to do so.
Having the care available increases the tax base and overall productivity. The businesses receiving the money add to overall employment and economic health. It is a net benefit for the economy and ends up with happier, better families and more profitable small businesses.
Seeing it just as a cost is dumb - the whole "hurr durr, this means tax and tax is bad" doesn't see the productive effects of the spending. It is far more productive than the biggest discretionary spending item, the military budget. Only looking at the cost side of the equation is just dumb. The same goes with single payer health care - yes it would mean more taxes, but the amount you and your employer pay for health care on your paycheck would be eliminated. For the vast majority of people this would be a net of more money in their check. For a few it would be less - those who don't have any insurance and those who may a huge amount and pay a tiny fraction for insurance
By the way, if the tax system actually taxed the wealthy in a sane way we could easily afford something like this. Billionaires don't get a W2 that says they earned a billion, their wealth never sees a taxable event. This is not because of any idea of fairness or balance, it is just that the system has loopholes and the wealthy can exploit them to their benefit.