Put cauliflower rice in a microwaveable bowl. Add about 2 tablespoons water. Cover with plastic wrap and microwave on high until tender, about 5 minutes. Let cool until safe to handle.
Lay a thin dish towel on a flat surface. Add 1/2 of cauliflower. Hold the 4 corners of the towel together to wrap up cauliflower completely. Twist the towel and squeeze hard to drain off as much water as possible. Remove cauliflower and repeat with other half.
Heat olive oil in a skillet over medium-high heat until smoking. Add cauliflower, onion, garlic, chili powder, cumin, and white pepper. Sauté, stirring constantly until cauliflower is browned and liquid is evaporated, about 5 minutes. Add salsa. Cook and stir until salsa is mostly reduced, 8 to 10 minutes more.