A depth of field that extends 10cm to infinity would suggest a lens focused at no less than 20cm. 

Since the lens has variable focus the optimal distance would be the minimum focus distance, which must be 20cm (or farther). Or the minimum distance where the subject fits w/in the field of view... just move it back as you stated. 

It is odd though that a DoF is defined for a variable focus lens as the DoF will vary depending at what distance the lens is focused. However, the DoF extending to infinity means that the minimum focus distance must be no less than the hyperfocal distance (2x minimum DoF limit).

The caveat to all of this is that we don't know what standard was applied to determine the camera's depth of field...  

And there is the possibility that the defined DoF is misidentified and should be *focus range* as noted in the comments by @scottbb... in that case the optimal distance is still the minimum focus distance, only that would then be 10cm instead of 20cm(+).