Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Beat cake mix, water, vegetable oil, and eggs together in a bowl using an electric mixer on low speed, about 30 seconds; increase speed to medium and beat until batter is evenly mixed, scraping sides of bowl as needed. Pour batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, 31 to 36 minutes. Cool cake in pan for 10 minutes before removing to a wire rack to cool completely. Keep oven at 350 degrees F (175 degrees C).
Beat milk and pudding mix together in a bowl until evenly combined and thickened; beat in cream cheese until filling is smooth. Fold whipped topping into filling.
Spread almonds and coconut onto a baking sheet.
Bake in the preheated oven until toasted and fragrant, 5 to 10 minutes.
Cut cake into bite-size pieces; spread 1 layer, 1-cube deep, into a trifle dish or glass bowl. Spoon a layer of filling, about the same depth as cake layer, over cake layer. Sprinkle a layer of almonds, coconut, and toffee bits over filling. Repeat layering with remaining ingredients.
