To a large bowl add the cream cheese and sweetened condensed milk. With an electric mixer, whip together cream cheese and sweetened condensed milk until smooth.
Add instant pudding and milk to the cream cheese mixture. Whip with an electric mixer until smooth and thick.
Fold in the whipped topping into the cream cheese mixture with a silicone spatula and mix until just combined.
Lay graham cracker sheets along the bottom of a 9x13 pan to form a full layer. Pour about ⅓ of the cream cheese filling over the graham crackers and smooth with a spatula until even. Add a single layer of strawberry slices over the cream cheese filling in the pan.
Repeat the layering of graham crackers, cream cheese filling and strawberries two more times, each time using ⅓ of the cream cheese mixture. On the top cream cheese mixture, add the prettiest strawberry slices for the last layer.
Refrigerate the icebox cake for 6-8 hours or overnight. Graham crackers will be soft, and the cream cheese mixture will have thickened and become more firm. Slice the cake and enjoy!
