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It’s likely that the book in The Babdook (2014) did exist, since Sam (Noah Wiseman) and Amelia (Essie Davis) both had physical interactions with it. It is also likely, however, that Amelia created the book. On the exterior, it didn’t look like a typical mass-produced, published book. It had a homemade quality to its construction. Further, during the birthday party scene, Amelia’s sister tells the other guests that Amelia used to write for a living. She mentions “some kids’ stuff” as being part of her former wheelhouse, implying she would have the skills necessary to craft a children’s book. Amelia also has inexplicably dirty hands in some early scenes, as if she’d been using charcoal, the medium in which the book was illustrated. Finally, after destroying the book, she finds herself with a repaired copy. She would know how to reassemble a book she created.

Paying attention to the language of the book’s narrative during Amelia’s first read-through also hints the book was created by her.

If it’s in a word or in a look - you can’t get rid of The Babadook.
See him in your room at night and you won’t sleep a wink.
I’ll soon take off my funny disguise, take heed of what you’ve read-
Once you see what’s underneath, you’re going to wish you were dead.

The narrative in the first two lines refers to the Babadook as “him” then switches to first-person in the next line, as if to say Amelia’s subconscious knows her breakdown is imminent.