In a mixing bowl, place the flour, tepid water, crumbled yeast and rub them in using the fingertips until getting a compact ball. Cover with a tea towel and leave to prove (1 to 2h depending on the room temperature).
Spread the dough on an oven tray and let it rise back. With the pointer finger make dips and wells on top of the dough.
In a glass, combine water, olive oil and coarse sea salt. Brush the focaccia with this mix and sprinkle with thyme. Bake for 40 minutes at 180°C (th. 6 - 350°F). Remove when lightly brown.
Blend all of the olive puree ingredients using a food processor.