Toast the slices of sourdough in a toaster or under a broiler until crispy and golden brown.
Rub the garlic clove halves cut side down on the toasted bread on both sides.
Cut the avocado in half, remove the pit and scoop the flesh into a mixing bowl.
Using a fork, mash the avocado to desired consistency. It should be smooth enough to be spreadable on the toast.
Season the avocado with salt and lemon juice to taste.
Spread a small portion of the avocado mixture on a slice of bread. Repeat with until all slices have avocado spread on them.
Arrange the toast on a serving plate. Top with olive oil, pomegranate seeds, and za'atar. Serve.