If using a boxed angel food cake, bake it according to the package directions, then let it cool completely before cutting it into even 1-inch cubes with a serrated knife. The cubes should look clean and springy, not mashed or ragged.
Whisk the instant vanilla pudding, milk, and sour cream together in a mixing bowl for a full 2 minutes, then set the mixture aside briefly. It should look smooth, thickened, and pourable, like a soft cream rather than thin milk.
Arrange half of the cake cubes across the bottom of a 9x13 baking dish in an even layer. Leave just enough space between pieces for the filling to settle around them.
Spoon about 2/3 of the cherry pie filling over the first cake layer, spreading it gently so the fruit lands across the surface instead of pooling in one corner. The cake should be dotted and lightly coated, not drowned.
Add the remaining cake cubes over the cherry layer, covering the fruit as evenly as possible. This second layer creates structure so the pudding can spread across the top without sinking too deeply.
Pour the pudding mixture over the cake and smooth it from edge to edge with a spatula. When it is spread evenly, the top will look creamy and level with no dry cake peeking through.
Spoon the whipped topping over the pudding layer and spread it into an even blanket. A light touch keeps the layers distinct and prevents the pudding from mixing into the topping.
Finish with the remaining cherry pie filling and toasted almond slivers, swirling the cherries lightly for a marbled look instead of stirring them in. The top should have streaks of red over white with almonds scattered for crunch.
Chill the dessert for about 4 to 5 hours before slicing and serving. The layers should feel set, and the cake will soften enough to cut cleanly with a spoon or knife.