It’s certain that the earliest manuscripts of the New Testament (e.g., Codex Sinaiticus) were written in uncials, but what about non-biblical manuscripts written by the earliest of the “Early Church Fathers.” Did they too write in uncials, or did they include minisculars when writing? I am primarily concerned with the autographs of both the Greek and Latin Church fathers.
It's impossible to tell whether the original manuscripts (the autographs) of any given sacred text were written in one hand, or the other, since as far as we are able to tell, none have survived unharmed to the present day. The earliest manuscripts we have in our possession, though early, are certainly already copies, and a copyist may change the hand of a document as they will.
That being said, in Late Antiquity, uncial was the formal hand for writing documents when you wanted them to be widely readable, from Ireland to Dalmatia (and beyond to Egypt, if you switched to Greek uncials), so that's what we get in manuscripts from that era — or at least those which were composed with enough quality and treated well enough that they managed to survive to our day.
So most of the earliest documents do, indeed, use uncial and not minuscule, which was reserved for private notes and letters. Given that, some of the earliest letters might have been indeed written in minuscule, but because they didn't survive, we can only speculate.