Yes, the government will subsidise this, although exact details vary, for example government might choose to arrange that they pay the employee over this period instead.
It's not magic, obviously overall the economy is still paying for this to happen, but then the US system isn't magic either, babies don't magically receive any benefits from parents who are actually working all the time and barely see them for a handful of hours per week. So the question is only: Is it a good idea? Because if it's a good idea then paying for it is just a question of mechanics. Same for universal healthcare, the provision of safe drinking water, literacy programmes, you name it.
It's not magic, obviously overall the economy is still paying for this to happen, but then the US system isn't magic either, babies don't magically receive any benefits from parents who are actually working all the time and barely see them for a handful of hours per week. So the question is only: Is it a good idea? Because if it's a good idea then paying for it is just a question of mechanics. Same for universal healthcare, the provision of safe drinking water, literacy programmes, you name it.