Preheat oven to 425 degrees F (220 degrees C).

Spray a skillet with cooking spray and add vegan crumbles. Cook and stir over medium heat until heated through and uniformly broken up, about 5 minutes. Stir in salsa and black olives. Remove from heat and cover to keep warm.

Spread taters on a baking sheet in a single layer.

Bake in the preheated oven for 10 minutes. Turn taters over; bake until crispy, about 10 minutes more.

Transfer taters to a shallow, oven-safe serving dish. Spread crumbles-salsa mixture evenly on top. Sprinkle vegan cheese on top.

Set oven rack about 6 inches from the heat source and preheat the oven's broiler.

Place baking dish in the oven. Broil, watching closely to prevent burning, until vegan cheese is melted, about 3 minutes.

Top with dollops of vegan sour cream.