Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Beat cake mix, water, oil, and eggs in a bowl with an electric mixer on low speed until moistened, about 30 seconds. Increase speed to medium and beat until combined, scraping the sides of the bowl as needed, about 2 minutes. Pour batter into the prepared baking dish.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 31 to 36 minutes. Remove from the oven; keep the oven on.

Cool cake in the pan for 10 minutes, then transfer to a wire rack to cool completely, about 20 minutes more.

While cake is cooling, spread almonds and coconut on a baking sheet.

Bake in the preheated oven until toasted and fragrant, 5 to 10 minutes; set aside until cake is cooled.

While cake, almonds, and coconut are cooling, beat milk and pudding mix together in a bowl with an electric mixer until combined and starting to thicken. Beat in cream cheese until smooth, then fold in whipped topping.

Cut cooled cake into bite-sized cubes. Combine cooled almonds and coconut with toffee bits in a bowl.

Layer 1/2 the cake cubes in the bottom of a trifle dish or glass bowl. Cover with 1/2 the pudding mixture, then 1/2 the almond mixture. Repeat layers once more.