Dissolve the yeast in a bowl with the sugar, water and half the flour. Cover with a moist cloth and leave to stand in a warm place for 15 minutes until foamy.
Stir the salt into the remaining flour, then tip into the yeast mixture. Stir with one hand to form a moist dough. Knead on a floured work surface for 10 minutes until smooth and elastic. It should be very soft and slightly sticky. If too sticky to handle, add a little more flour. Put in an oiled bowl, cover with a moist cloth and leave to rise in a warm place for 1 hour, or until doubled in size.
Gently knead half the onion and olives into the dough. Transfer to a lightly oiled rectangular baking tray, about 20 x 30 cm (8 x 12 inches), stretching it to fill the tray. Cover with a moist cloth and leave to rise in a warm place for 30 minutes. Make deep dimples on the surface with your finger. Scatter with the rosemary and remaining onion and olives and drizzle with oil. Cover again and leave to rise for 15 minutes.
Sprinkle the top of the focaccia with coarse sea salt. Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 20 minutes. The bread is ready when the base sounds hollow when tapped. If not, bake for a further 5 minutes. Turn out on to a wire rack and leave to cool. Eat warm or at room temperature on the same day.