Preheat oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a large bowl, mix flour, sugar, baking powder, baking soda, and salt.
Add almond milk, vegetable oil, apple cider vinegar, and vanilla extract. Mix until smooth.
Pour batter into the prepared pan and bake for 30 minutes or until a toothpick comes out clean.
In a separate bowl, combine coconut milk, evaporated coconut milk, and sweetened condensed coconut milk.
Once the cake is done, poke holes all over the cake with a fork and pour the milk mixture over the cake.
Refrigerate for at least 4 hours or overnight before serving.