Ok, fine. They still have to inherit that money. But as they grow up, the rich baby will have access to better nutrition, better education, a less stressful environment, etc compared to the poor baby. That's without considering fetal health/nutrition. There are many known factors that can affect a child's health, growth, and intelligence, and therefore success.
I don't think the distinction of "babies have $0" is relevant when considering all the other potential advantages. What are you getting at with that claim? I don't think it's particularly clear, judging by the other replies.