Well, first, you should know that bulging eyes are well known as Proptosis, or exophthalmos. And it can occur in adults or babies. For many people, it is the bulging out of one or both bilateral of the eyes. And we can say that there should be no visible white between the top of the iris, which is the colored part of the eye, and the upper eyelid. In some situation when you can see white in this area, it is usually a sign of bulging eyes. Of course, it will just like your baby gets. For the causes, glaucoma, Graves Disease, Hemangioma, Histiocytosis can be possible. And if your baby has it, I will suggest you take your baby to see the eye doctor as soon as possible, for it is considered a very serious problem.