Start by greasing a 9x13-inch pan to prevent sticking. In a mixing bowl, combine graham cracker crumbs, granulated sugar, and melted butter. Use a fork to mix until the mixture resembles wet sand. Press this mixture firmly into the bottom of the pan to form an even layer. Refrigerate for 30 minutes to set the crust.

In a medium saucepan, combine the granulated sugar and cornstarch, then stir in cold water. Bring this mixture to a gentle boil over medium heat, stirring constantly until it thickens and becomes translucent. Remove the pan from the heat, then dissolve the peach Jello powder into the thickened mixture until fully combined. Fold in chopped fresh peaches, and let this topping cool in the refrigerator for about 20 minutes.

In a mixing bowl, beat softened cream cheese and powdered sugar together using an electric mixer until smooth and creamy. Gradually fold in the whipped topping, mixing gently until everything is well combined and fluffy. Spread this filling evenly over the chilled graham cracker crust.

Once the peach topping has cooled slightly, pour it gently over the cream cheese filling, making sure to spread it evenly. Cover the pan with plastic wrap and refrigerate for 4 to 5 hours until the dessert is thoroughly set.

Slice the No-Bake Fresh Peach Cheesecake Dessert into squares using a sharp knife. Consider adding a dollop of whipped topping on each piece for an extra touch of creaminess. Serve immediately.