In a large bowl, whisk together the coconut cream pudding mix and milk until smooth. Continue mixing until it thickens, about 1 minute.
Fold in one container of whipped topping until fully combined.
Layer ¼ of the graham crackers in the bottom of a 9×13-inch dish, breaking them as needed to fit.
Spread ⅓ of the pudding mixture evenly over the crackers.
Repeat the layering process two more times.
Add the final layer of graham crackers on top.
Spread the remaining whipped topping over the top, covering all crackers.
Cover and refrigerate the Coconut Icebox Cake for at least 6 hours, preferably overnight.
Sprinkle toasted coconut on top before serving.