Step 1
Place potato into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender about 20 minutes. Drain and rinse under cold running water.
Step 2
Peel potato; mash in a large bowl with a fork. Pour in flour and mix well with your fingertips. Rub together until mixture is even and free of lumps.
Step 3
Combine 1 cup water yeast and sugar in a bowl. Mix well and let stand until frothy about 5 minutes. Stir in 5 tablespoons olive oil.
Step 4
Pour yeast mixture over flour mixture; mix adding remaining 1 cup water a little at a time until a soft dough forms. Mix in 1 tablespoon salt.
Step 5
Knead dough on a clean work surface until smooth and soft 8 to 10 minutes. Transfer dough to a greased bowl. Cover with a damp cloth; let rise in a warm place until doubled about 2 hours.
Step 6
Grease a large rimmed baking sheet with 2 tablespoons olive oil. Place dough on the baking sheet; stretch into the corners. Arrange tomatoes and olives over dough.
Step 7
Mix remaining 1 tablespoon olive oil and 2 tablespoons water together in a bowl. Brush mixture over dough. Sprinkle remaining 1 tablespoon salt on top. Cover with a damp cloth; let rise for 30 minutes.
Step 8
Preheat oven to 400 degrees F (200 degrees C).
Step 9
Bake focaccia on the lower rack of the preheated oven for 15 minutes. Lift up with a fork to check bottom is golden brown. Transfer to the middle rack and bake until top is golden 10 to 15 minutes more. Sprinkle oregano on top.