Preheat the oven to 350°F (175°C). Lightly grease a 9×5-inch loaf pan and line it with parchment paper, leaving an overhang on the sides for easy removal.
Grate the zucchini using a box grater or food processor. Place the grated zucchini in a clean kitchen towel and squeeze out as much moisture as possible. Set aside.
In a medium bowl, whisk together the gluten-free all-purpose flour, almond flour, baking soda, baking powder, salt, cinnamon, and nutmeg until well combined.
In a large bowl, whisk the granulated sugar, brown sugar, eggs, vegetable oil, applesauce, and vanilla extract until smooth and well combined.
Add the dry ingredients to the wet ingredients and gently fold together until just combined. Do not overmix.
Fold in the grated zucchini until evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Remove the bread from the oven and allow it to cool in the pan for 15 minutes.
Using the parchment paper overhang, lift the bread out of the pan and transfer it to a wire rack to cool completely before slicing.