The phrase "any baby with a capital H" likely refers to the concept of "Baby" in the context of a story or theory, perhaps related to literature, psychology, or cultural studies. Without additional context, it's hard to specify exactly what you mean.
However, if you hint that "any baby" represents innocence, potential, and a new beginning, then a baby—be it depicted in a story, or symbolically—often embodies pure potential, a fresh start, and the hope for the future.
If you meant something else by "capital H," please provide more context so I can give you a more accurate answer!