In a small bowl, stir together the lukewarm water, yeast and sugar. Let stand until foamy, 3 to 5 minutes.
Using a stand mixer, mix the flour and salt at low speed. Mix in the yeast mixture and olive oil until a shaggy dough forms. Switch to dough hook and mix at speed 2 for 6-8 minutes.
Transfer the dough to a greased, large mixing bowl, turning to coat; cover and let rise 45 minutes to an hour at room temperature or overnight in the refrigerator.
When the dough has doubled in size (or the next day, if refrigerated), remove the dough from refrigerator and press into a greased 10-inch cast-iron skillet. Let rise until doubled in size (20 -30 minutes if proofed at room temp or 60-90 minutes if proofed in the fridge).
Preheat oven to 400°F. Top dough with tomato sauce, cheese and sausage. Bake for 25 minutes. Let cool in the pan for 5-10 minutes before serving.