In a large bowl, dissolve the sugar in warm water. Sprinkle the yeast over the water and let it sit for about 5 minutes, or until it becomes frothy.
Add 2½ cups of flour, salt, and olive oil to the yeast mixture. Stir until a sticky dough forms. Gradually add the remaining flour as needed until the dough comes together but is still slightly tacky.
Turn the dough out onto a floured surface and knead for about 8-10 minutes, until smooth and elastic.
Place the dough in a greased bowl, covering it with a damp cloth. Let it rise in a warm place for about 1 hour, or until doubled in size.
Punch down the dough and shape it into a loaf that will fit your air fryer basket. Let it rise again for about 30 minutes, or until puffy.
Preheat your air fryer to 350°F (175°C) for about 3 minutes.
Place the dough in the air fryer basket. You may line the basket with parchment paper if desired. Air fry for about 20-25 minutes, or until the bread is golden brown and sounds hollow when tapped.
Remove the bread from the air fryer and let it cool on a wire rack before slicing to ensure the interior finishes cooking with residual heat and sets properly.