Process the chocolate sandwich cookies in a food processor until fine crumbs form. Do not remove the cream centers before processing.
Transfer the cookie crumbs to a large mixing bowl. Add the softened cream cheese and blend thoroughly with a spatula or hand mixer until a thick dough forms.
Roll the mixture into 1-inch balls (making about 36 balls) and place them on a parchment-lined baking sheet. Freeze for 30 minutes to firm up.
Melt the white candy melts in a microwave-safe bowl in 30-second intervals, stirring in between, until completely smooth.
Remove the chilled balls from the freezer. Dip each ball into the white coating using a fork or dipping tool, tap off the excess, and return to the parchment paper.
Melt the red and blue candy melts in separate bowls using the same 30-second interval method. Drizzle the red and blue coatings over the white truffles.
Immediately top with white star sprinkles before the red and blue drizzles harden. Chill in the refrigerator for at least 15 minutes to fully set before serving.