The vast majority of the EU does not offer anything close to free universal early childhood care like this. None of Western Europe. I can think of only Latvia and Romania off the top of my head.
It's not quite free in every state, although it's closer to that than many people here probably realize.
At least until 2025 (unsure how the July budget cuts will affect this longer-term), Medicaid provides free or low-cost insurance to eligible children/families, which in theory should apply to everyone who isn't eligible for health insurance through other means. Emphasis on in theory, though - in practice, there are plenty of people who aren't covered.
It's probably more accurate to say that almost all children are eligible for healthcare coverage, and that coverage is free or low-cost for millions of people who meet various income thresholds. (People who are covered on private insurance almost always have copays or deductibles, so it's not truly free for them because there is some out-of-pocket cost).