Place shredded zucchini in a colander over the sink. Sprinkle with salt, toss gently, and let sit for 10 minutes. Transfer to a clean kitchen towel and squeeze firmly until no more liquid comes out. Repeat if needed.
Preheat oven to 400°F (200°C). Grease a 13x9-inch baking dish with nonstick cooking spray.
In a large bowl, combine the drained zucchini, eggs, Parmesan, and half the mozzarella and cheddar. Mix until evenly combined.
Press the zucchini mixture evenly into the prepared baking dish, spreading it all the way to the edges. Bake for 20 minutes until set and lightly golden at the edges.
While the crust bakes, cook the ground beef and chopped onion in a large skillet over medium heat, breaking the meat apart, until no pink remains — about 8 to 10 minutes. Drain excess fat.
Add the minced garlic and cook for 1 minute, stirring constantly. Pour in the tomato sauce or marinara, stir to combine, and simmer for 2 to 3 minutes until slightly thickened.
Spoon the meat sauce evenly over the baked zucchini crust. Scatter the remaining mozzarella and cheddar over the top.
Return the dish to the oven and bake for another 20 minutes, until the cheese is fully melted, golden, and bubbling.
Remove from the oven and let rest for 5 minutes before slicing into 8 portions. Serve directly from the dish.