In a large mixing bowl, whisk together instant pudding mix and cold milk for 2 minutes until it thickens. Add sweetened condensed milk and whisk until smooth and creamy.
Slice bananas into ¼-inch rounds. If not assembling right away, toss lightly with a splash of lemon juice to keep from browning.
In a 9x13-inch dish or trifle bowl, spread a thin layer of pudding on the bottom. Add a single layer of Nilla wafers. Top with banana slices.
Spoon more pudding over the bananas to cover them completely. Repeat layers: wafers, bananas, pudding—until you run out, ending with pudding on top. Aim for 3-4 layers.
Spread whipped topping evenly over the top. Crush a few extra Nilla wafers and sprinkle on for garnish.
Cover with plastic wrap and refrigerate 4 hours or overnight so wafers soften slightly and flavors meld.
Scoop or slice and serve cold. Keep leftovers in the fridge.