Prepare and bake the red velvet cake in a 9x13-inch pan according to package instructions. Let cool slightly.
Using the end of a wooden spoon, poke holes all over the warm cake.
In a medium bowl, whisk together the pudding mix and cold milk until smooth and slightly thickened.
Pour the pudding mixture over the cake, making sure it fills the holes. Smooth the top with a spatula.
Refrigerate the cake for at least 1 hour to allow it to set.
In a large bowl, beat the softened cream cheese and powdered sugar until smooth. Fold in the whipped topping until fully combined.
Spread the cream cheese topping evenly over the chilled cake.
Top with crushed red velvet cake crumbs or sprinkles if desired. Serve chilled.