Lightly grease a 9x13 pan to prevent sticking. In a mixing bowl, combine graham cracker crumbs, granulated sugar, and melted butter. Stir until evenly moistened, then press this mixture firmly into the bottom of the pan to form a crust. For a firmer base, refrigerate for 30 minutes, or to save time, bake at 375°F for 8 minutes, and then let it cool.

In a medium saucepan, mix together granulated sugar and cornstarch. Gradually add cold water while stirring, and heat over medium to high heat until the mixture begins to boil and thicken, which should take around 1-2 minutes. Remove from heat, then stir in the Peach Jello until fully dissolved before gently folding in sliced fresh peaches. Set aside to cool, then refrigerate for about 20 minutes.

In a clean mixing bowl, beat together softened cream cheese and powdered sugar using an electric mixer until the mixture is smooth and fluffy, about 2-3 minutes. Gradually add in whipped topping and vanilla extract, mixing until fully combined and airy. Once ready, spread this creamy filling evenly over the chilled crust, ensuring an even layer throughout.

Take the cooled peach topping out of the refrigerator. Pour the peach mixture carefully over the cream cheese layer, allowing it to spread naturally across the surface. Make sure the peach slices are evenly distributed for an attractive top. Now, cover the pan with plastic wrap and refrigerate for 4-5 hours, or until fully set and firm to the touch.

Once the no-bake fresh peach cheesecake dessert has set, remove it from the fridge and cut into squares. For an added touch, serve with a dollop of whipped topping on each square for extra creaminess.