In a large bowl combine the flour, yeast, and salt. Add the water and stir with a large spoon until the flour is completely incorporated. You may need to get your hands in there to finish mixing in the flour. The dough will be wet and sticky. Cover the bowl with plastic wrap and let it sit in a warm spot in the kitchen for 10-12 hours.
As soon as you are done mixing the dough, make the garlic oil. Heat oil on medium heat with the garlic. Once it starts bubbling, reduce the heat to low and cook for 5 minutes. The garlic will be soft and lightly golden. Using a slotted spoon, scoop the garlic out of the oil. At this point you can either toss the garlic or reserve it to work into the focaccia. Let the oil cool to room temperature.
Once the dough is covered in bubbles and looks puffy the dough is ready to be shaped.
Take 2 tablespoons of the oil and put it into a 10 or 12 inch cast iron skillet. Using your fingertips, scrape the dough out of the bowl into the skillet and turn it to coat it with oil. Spread out the dough over the bottom of the skillet. If it doesn't reach the edges, wait about 10 minutes and then gently push it out some more.
Cover the skillet with plastic wrap and let the dough rest for 1 hour.
After 30 minutes, set a rack to the lower middle position and turn on the oven to 500F.
When ready, top the dough with more of the garlic oil. Then sprinkle thyme leaves, coarse salt, and the reserved garlic slice (if desired) over the top. Dimple the dough with your fingertips, working some of the toppings down into the bread.
Bake until the middle is cooked through, the top is brown, and the bottom is crispy. 15-20 minutes in a 12-inch skillet. 20-25 in a 10-inch skillet.