Heat olive oil in a small frying pan over medium heat. Add chile powder and turkey and toss to coat. Cook until turkey is heated through, 2 to 3 minutes. Remove from heat.
Spread 1/4 cup mashed sweet potato on each tostada shell. Spoon cranberry sauce over sweet potato, then divide turkey between tostadas. Top each with crema and a squeeze of lime, then sprinkle with green onions and cotija cheese.