How is it possible that all animals were once Herbivores?

I'm referring to the Bible and Creationists. I've heard many times that all animals were once herbivores...but how is this possible? Members of the carnivora order (includes cats, dogs, bears, etc.) are specifically built to be carnivores! They all have claws, sharp teeth, enhanced senses. Did God make them this way when he first created animals, or did they all of a sudden develop these whenever carnivores came about?