As far as we know from archaeological finds and iconography, warriors of the early middle ages (in Europe at least) wore no hand protection at all. They definitely did not wore bracers of any kind (this is pure reenactorism for safety sake). Bracers of this kind were used almost exclusively by Asian cultures at this point in history. The idea that EMA warriors wore bracers comes from a misunderstanding of iconography: what appears as bracers on the tapestries and frescoes of that era are actually decorative cuffs of the tunic peaking from underneath the top layer of clothing.

In fact, the majority of warriors up until 11th century wore no armour at all, except (possibly) padded woolen tunics. Boiled leather armour was not yet reasonably possible back then, and chainmail was prohibitively expensive, and so were helmets.

The closest possibility of armoured gauntlets would be among the upper crust of Byzantine warriors, but this is pushing both your timeline (that would be the very latest part of Early Middle Ages as we understand them) and almost outside Europe (beyond which the term "Early Middle Ages" is not applicable).

From osteological research we know that hand injury were not all that common. The most common injury was to the upper arm, ribs on the right side, right thigh and knee, and occasionally neck/side of the face. Off the top of my head I cant think of a single example of a post-battle skeleton from that period found missing digits or parts of the hand from being cut.

Actual Early Medieval combat was sufficiently different from reenactment combat that the type of injury would be different, and injury to the hand would be superficial.