What causes a blue sclera in infants?

Thin sclera: The layer under the sclera is called the choroid and is darkly pigmented. In infants (and old people) the sclera can be thin and the dark pigment shows through. Alternatively, it could be a nevus (blue nevus of ota) in which case you need to have it checked out since it can be associated with other conditions.

Vessles: The thinness of the layers of the eye allow the hue of the blood vessels below to be seen and therefore the blue sclera.