In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until it's light and fluffy, about 2-3 minutes. Make sure there are no lumps for a smooth pie.

Add the sweetened condensed milk, fresh lemon juice, and vanilla extract to the cream cheese mixture. Beat on low speed until just combined and smooth, scraping down the sides of the bowl as needed.

Open the can of sliced peaches and drain them very well. You can even gently press them in a fine-mesh sieve or blot them with paper towels to remove excess moisture, which is key for a firm pie.

Gently fold the thawed whipped topping (Cool Whip) into the cream cheese mixture using a spatula, until no streaks remain. Be careful not to deflate the mixture too much, keeping it light and airy.

Carefully fold in the well-drained sliced peaches into the filling. Ensure they are evenly distributed throughout the mixture.

Spoon the peach filling evenly into the pre-made graham cracker pie crust. Smooth the top with the back of a spoon or spatula.

Cover the pie loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until it is fully set and firm enough to slice cleanly. This chilling time is essential for the pie to hold its shape.