Right, I understand that there was not a permanent MG mounting on the StuG III's until the G version came about in late '42/early '43.
However, since the StuG was vulnerable to infantry attack, a portable MG34 was frequently carried onboard to fend off anti-tank troops, even on the earliest model A's. This "deficiency" of not having a more convenient mounting was rectified with the creation of the mark G.
Here is a photo of a mark F with the loader riding on the hull with his MG34. The middle pic is of a mark F long barrel taken in the Don river area near Voronezh, Summer of '42. The bottom is of my custom StuG III F set to make its debut on my map.