Yup, a hawk could totally kill a baby goat. Might not be able to fly off with the whole thing, depending on the breed of goat/species of hawk, but if it was hungry and the goat was an easy target, there's no reason one wouldn't. I won't let my mini babies out for a month and even then they have a pen, because the resident Cooper's could easily snag them.
A fox is also a very real danger, and can grab, kill and carry off a newborn goat of any breed, or a lamb, too.