It’s true that Hugo transforms over the course of The Invention of Hugo Cabret—after all, we see actual images of him as a boy, and then as a boy with a haircut who looks older and more put together. But there are a lot of other transformations going on in the book, if you care to look hard enough. Georges Méliès transforms from a lonely, bitter old man to someone who embraces both his past and his future. And Hugo transforms from a lonely orphan to a well-loved member of a family. Even the automaton transforms from a pile of junk outside a burnt-down museum to a beautiful, amazing contraption.
Over the course of the book, Georges Méliès transforms from a tired old man back into the exciting magician he used to be because Hugo reminds him of what it means to truly be yourself.
The automaton and the quest to fix it transform Hugo, if not into a man, then at least a more mature boy.