Preheat oven to 350F and line an 8 x 13 " baking pan with parchment paper, and spray lightly with oil.
In a small bowl, combine the soy milk and apple cider vinegar. Mix to combine.
In a medium bowl, combine the all-purpose flour, sugar, baking powder, and baking soda. Mix well.
Add the milk-vinegar mixture to the bowl with the flour mixture, add the oil, and vanilla, and whisk to combine. Set aside.
In a large bowl, pour in the aquafaba and using a stand mixer with the whiks attachementor a hand-held mixer whip at medium-high speed until soft peaks form, about 4 minutes.
Pour the whipped aquafaba into the bowl with the cake batter, and fold it in with a spatula until it has completely incorporated into the cake batter.
Pour the batter into the baking dish and bake in the middle rack of the oven, for 25-30 minutes or until an inserted toothpick comes out clean.
Remove from oven. Let cake cool for 10 min, and remove from baking dish. Remove parchment paper and let cake cool completely on a rack.