Preheat the oven to 350 degrees F (180 degrees C). Grease an 8-inch by 8-inch baking pan and line it with a sheet of parchment paper.
Add the pumpkin puree, milk, egg, oil, and maple syrup to a bowl and whisk until smooth.
To the same bowl, add the flour, baking powder, baking soda, and pumpkin pie spice and mix until smooth. Do not overmix. It is okay if there are a few lumps in the batter.
Pour the mixture into the prepared 8-inch by 8-inch pan.
Bake the cake for 30 to 35 minutes, or until an inserted knife or toothpick comes out clean. Allow the cake to cool completely
Once the cake is cooled, spread the cream cheese frosting on top of the cake. Slice and serve!