Preheat oven to 400°F. Halve acorn squash, de-seed, and slice into crescents. Rub each slice with olive oil and set on a foil-lined baking sheet. Bake until easily pierced with a fork, about 20 minutes. Let cool, then diced into 1-inch chunks.
Turn oven up to 475°F.
Roll out pizza dough. Drizzle olive oil across dough, then scatter squash, figs, and goat cheese on top. Cook for about 12 minutes, until dough is browned and cheese has softened.