Pour in the water, wine, olive oil, herbs, salt, and Parmesan in the bowl with the sponge. Mix thoroughly until well combined.
Add in the flour, beating with a wooden spoon until the mixture is smooth and very soft.
Knead the dough by pulling it up and folding it over for 5-6 minutes until it becomes smooth and elastic. If the dough is too wet, you can add up to 1/2 cup flour.
Leave the dough in the bowl, cover with a damp tea towel, and let it rise until doubled in size and full of bubbles, about 1 ½ to 2 hours.
Once risen, press the dough into a lightly oiled and parchment-lined 8-inch round or square cake or springform pan.
Cover the dough again with a damp cloth and let it rise until doubled, about 1 - 1 1/2 hours.
Preheat the oven to 400°F (200°C) about 30 minutes before the dough is ready.
Using oiled fingers or knuckles, press deep dimples into the surface of the dough.
Drizzle a couple of tablespoons of olive oil over the dough, allowing it to pool in the dimples.
Sprinkle with coarse sea salt.
In a small bowl, toss the red onion slices with a teaspoon of olive oil.
Arrange the red onions and fig halves on top of the dough.
Sprinkle a bit of sugar over the figs.
Scatter fresh thyme leaves over the top of the focaccia.
Allow the focaccia to sit for 20 minutes.
Bake on the middle rack for 15 minutes at 400°F (200°C), then reduce the heat to 375°F (190°C) and bake for an additional 25 to 30 minutes, or until golden brown.
Remove from the oven and let cool on a wire rack.