That is a question for the ages, for it seems that as long as humans have had access to both stale bread and milk, they’ve put the two together and baked them. Bread pudding predates the concept of sweet pudding as we know it, probably by millennia. Virtually all our modern dessert puddings are descendants of sausages. They’re the sweet grain-based cousins of blood-and-offal mixtures that were traditionally stuffed into bladders and boiled. These so-called “white puddings” only became widespread in Europe in the 1600’s when the pudding cloth was invented.
Bread pudding is much, MUCH older. It goes back past the Romans, past the Greeks, probably even past the Egyptians who enjoyed a variant which (today) goes by the name of Om Ali, a mixture of milk, bread, raisins and nuts. Indian shahi tukra is a very similar thing, a preparation of fried bread sweetened with syrup and cream. You know, I’d be willing to bet that wherever you find bread-baking livestock-herding societies on Earth, you’ll probably find a traditional bread pudding-like dish. It’s that good an idea.