Dogs evolved the capacity to eat a more starchy diet than their wild relatives largely because of their close association with humans, who are of course omnivorous. On the other hand, the branch of canis that became "wolves," etc. largely stayed away from humans and remained carnivorous. Almost certainly, at first, as early "dogs" began essentially living in human camps they would likely have eaten scraps of meat left over after the humans ate. But because humans also ate other things, those dogs would have started to eat them as well and gradually their systems became accustomed to them. By the time of the New Testament, dogs were largely seen as scavengers (as they're still seen in some parts of the world) who would basically eat whatever they could find - usually living in close contact with humans (although not as pets in NT times) because of the abundance of food scraps available. There's the story in the Gospels, for example, of the woman who begs Jesus for help, reminding him that even the dogs get the crumbs from the table - the crumbs would not just have been meat scraps, but whatever bits of food of any kind were left over.
