Preheat your oven to 350°F (175°C). Grease a baking pan.
In a mixing bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
Add almond milk, vegetable oil, apple cider vinegar, and vanilla extract. Mix until smooth.
Pour the batter into the prepared baking pan and bake for 30 minutes, or until a toothpick comes out clean.
While the cake is baking, mix together coconut milk, almond milk, and sweetened condensed coconut milk in a bowl.
Once the cake is done, let it cool for 10 minutes. Poke holes all over the cake with a fork.
Pour the milk mixture over the cake, ensuring it soaks in. Refrigerate for at least 2 hours before serving.