Hi, I am sorry but that is not possible with mesh objects. If there is no other format available, the only solution is to nudge it onto the midpoint by eyeballing it.
In that case if you have the logo in a CAD format or in DXF/DWG, the workflow is much more precise. After extruding the logo, an additional modeling element can help a lot in aligning the logo to the exact midpoint of the chosen face. If you have time, please take a look at the video below: