Wash, dry, and cut the sweet potato into several long slices of similar thickness to bread slices. Evenly brush each slice of sweet potato with olive oil. Microwave: Place the sweet potato slices on a plate and microwave for about 2-4 minutes (depending on the power of your microwave). Check occasionally to see if they are done. Remove when they are browned. Meanwhile, prepare the remaining ingredients. Oven: Place the sweet potato slices on a baking sheet lined with parchment paper and put them in an oven preheated to 180°C. Remove when the slices are slightly softened and browned, about 10-15 minutes. Meanwhile, prepare the remaining ingredients.
Wash, dry, and cut the avocado in half lengthwise. Drizzle the half with the pit with lemon/lime juice, wrap tightly in plastic wrap, and place in the refrigerator (use within a few days for another meal). Scoop out the flesh from the other half with a spoon. Place in a bowl and mash with a fork. Add peeled and pressed garlic, and season with salt and pepper to taste. Wash, dry, and cut the tomato into half-slices. Spread the avocado paste on the prepared sweet potato slices.
Arrange the tomato slices on the toasts.