Put cookie dough onto a 12-inch pizza pan, rolling to fit to the edges in an even layer.
Bake cookie dough 'crust' in preheated oven until golden brown, 10 to 14 minutes. Cool crust at room temperature until cool enough to handle. Carefully slide spatula under the 'crust' and remove from pan to a large, flat serving platter.
Whisk 1 cup milk and pudding mix together in a bowl until smooth; put aside until set.
Beat cream cheese and 1/2 cup milk together in a separate bowl. Add pudding mixture to the cream cheese mixture and stir until smooth; spread evenly over the 'crust.'
Stir margarita mix, sugar, and cornstarch together in a saucepan over medium-high heat; cook and stir until the sugar dissolves completely and the mixture thickens into a syrup. Remove from heat to cool slightly. Stir strawberries into the syrup; pour onto the pizza 'crust' and spread evenly.
