With the plane set to take a not-very-thin shaving, the mouth is 0.006” (six thousandths of an inch, a sheet and a half of paper). Paradoxically, the deeper the cut, the smaller the mouth gets (since the bevel gets thicker as the blade is pushed into the mouth).
You can see that I’m not all that concerned with a polished sole. This was flattened on a medium India oil stone. I start out with PSA (sticky backed) sand paper on a flat surface but I’ve never gotten anything truly flat that way so I finish up with other methods (such as the oil stone, diamond plate or sand paper on a long stick (better control of material removal)).