In a stand mixer, mix together water, olive oil, sugar, and yeast. Allow the yeast to bloom, approximately 5 minutes.
Add in the sourdough discard, making sure it’s at room temperature.
Slowly add the salt and flour to the liquids until it comes together.
Turn the dough out onto a floured surface to knead by hand or use a dough hook in a stand mixer for 3-5 minutes.
Drizzle a little more olive oil on the dough and move the dough around to be coated. Cover with a damp tea towel or plastic bag and let rest until doubled in size.
Divide the dough into two for thin crust pizza or make one thick crust pizza.
Roll out the dough onto a cookie sheet or baking stone, let rest while the oven preheats to 400°F.
Finish one of two ways:
Bake for 12 minutes, then add toppings and bake for 5-8 minutes more until cheese is melted.
OR - top the dough with everything and bake for 15-20 minutes until crust browns and cheese is bubbly.