In a large mixing bowl, whip the chilled coconut cream, powdered sugar, and vanilla extract until stiff peaks form.
Spread a thin layer of the whipped coconut cream on the bottom of a 9x13 inch baking dish.
Arrange a single, even layer of gluten-free dairy-free sponge cake slices over the cream.
Top the cake layer with half of the sliced strawberries and a third of the blueberries.
Spread a thick layer of whipped cream over the berries, then repeat the layers (cake, berries, cream) until all ingredients are used, finishing with a layer of cream topped with the remaining fresh berries.
Cover the dish tightly and refrigerate for at least 4 hours, or overnight, to allow the cake layers to soften.