Thank you everyone for the replies! It is a "C" serial number but sadly, ISMACS says almost nothing about them except "Beginning 1908." And something about the Russian army destroying a lot of Singer's equipment in 1945.
I checked out the thread comparing the 115 to the 15, but unsurprisingly it just succeeded in confusing me even more, haha. Because I truly don't know anything about old machines and at first wasn't even sure how to find the bobbin area! But I did take a couple of other shots of the parts showed in the pictures on that thread ... the bobbin winder does look exactly like the 115 in the picture but the bobbin area itself look more like the 15. The other bits look different enough as to be inconclusive ... at least in my brain anyway!
As you can see, this old machine needs some TLC ... the bobbin area in particular is pretty rusty!