Combine graham cracker crumbs, 2/3 cup sugar, and melted butter in a mixing bowl. Mix until evenly moistened, then press into the bottom and halfway up the sides of a 9-inch springform pan. Place pan on a baking sheet.
Bake the crust in the preheated oven until lightly browned and toasted, about 10 minutes. Remove from the oven and allow crust to cool.
Beat cream cheese and 1/2 cup sugar together in a large bowl with an electric mixture until light and fluffy, 2 to 3 minutes. Beat in pumpkin puree until completely incorporated.
Fold whipped topping into pumpkin mixture; stir in nutmeg and pumpkin pie spice. Pour pumpkin mixture into graham cracker crust. Cover pie with plastic wrap and refrigerate overnight. Gently remove pie from springform pan.