Cut the turkey into 1 1/2-inch pieces. Sprinkle with the cumin, and salt and pepper to taste. Heat the olive oil in a Dutch oven or large pot over high heat. Add the thyme, then add the turkey and cook until browned on one side, about 3 minutes. Add the onion and cook, stirring occasionally, until softened, about 4 minutes.
Stir in 5 cups hot water, the potatoes, butternut squash, zucchini, salsa and tostadas (the tostadas will dissolve and help thicken the broth). Cover and bring to a boil, then uncover and reduce to a simmer. Cook until the vegetables are tender and the turkey is just cooked through, about 15 minutes. Serve with more tostadas.