Grease a 9-by-13-inch baking dish and spread the cubed eggless bread evenly inside. Scatter the raisins over the bread.
Whisk the whole milk, heavy cream, sweetened condensed milk, cornstarch, melted butter, vanilla extract, cinnamon, nutmeg, and fine salt until smooth.
Pour the custard mixture evenly over the bread. Gently press the bread into the liquid and let it soak for 30 minutes.
Preheat the oven to 350 degrees F. Mix the turbinado sugar with the remaining cinnamon and scatter it over the soaked bread.
Bake for 40 to 48 minutes, until the edges are puffed, the top is crisp, and the center is set but still moist.
Cool the bread pudding for 15 minutes before serving. The custard will thicken as it rests while the middle remains soft and creamy.