Preheat the oven to 350°F.
Grease a 9x13-inch baking dish thoroughly.
In a large mixing bowl, combine the granulated sugar, eggs, and vanilla extract.
Beat the mixture until it is smooth, light, and fluffy.
In a separate small bowl, sift together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the egg mixture.
Mix only until the batter is just combined. Do not overmix.
Pour the batter into the prepared baking dish.
Spread the batter evenly in the dish.
Bake for 30 to 34 minutes, or until a toothpick inserted into the center of the cake comes out clean.
While the cake is baking, prepare the dairy-free milk mixture.
In a large bowl, combine the unsweetened canned coconut milk, almond milk, and sweetened condensed coconut milk.
Whisk until the milk mixture is smooth and fully combined.
Remove the baked cake from the oven.
While the cake is still warm, use a fork to pierce the top of the cake evenly over the entire surface.
Slowly pour the prepared dairy-free milk mixture over the warm cake.
Allow the milk mixture to soak into the cake.
Let the cake cool completely to room temperature.
Once cooled, cover the baking dish.
Refrigerate the cake for at least 8 hours, or overnight.
Place the cans of coconut cream in the refrigerator during this chilling time.
When ready to prepare the topping, do not shake the chilled cans of coconut cream.
Carefully open the cans and spoon the solid coconut cream from the top into a large mixing bowl.
Set aside the liquid remaining at the bottom of the cans for another use.
Whisk the coconut cream solids until smooth.
Add the powdered sugar and vanilla extract.
Whisk until the topping is creamy, smooth, and spreadable.
Spread the coconut whipped topping evenly over the chilled cake.
Dust the top with ground cinnamon, if desired.
Refrigerate the cake until ready to serve.
Slice and serve chilled.