In a blender or food processor, beat the softened cream cheese until smooth, then add the sweetened condensed milk, evaporated milk, and reserved peach syrup, blending until fully incorporated.
8 oz cream cheese, 1 can sweetened condensed milk, 1 can evaporated milk
With the blender running on low, slowly pour in the fresh lime juice. Blend until the mixture visibly thickens.
½ cup fresh lime juice
Pour a thin splash of the cream mixture into the bottom of a 9x13-inch baking dish (or a deeper 8x8 dish if you prefer higher, extra-thick layers), spreading it evenly to keep the bottom layer of cookies from sliding.
Arrange a single, flat layer of Maria cookies across the bottom of the dish, breaking a few cookies to fill in any open gaps.
2 packages Maria cookies, 1 can sliced peaches
Spread a portion of the thickened lime-cream mixture over the cookies, then top with a layer of sliced peaches.
Continue layering the cookies, cream mixture, and peaches—using up your ingredients and finishing with a smooth layer of cream and diced or sliced peaches on top.
Cover tightly with plastic wrap and refrigerate for at least 4 to 6 hours, ideally overnight.
Slice and serve cold.