Per the spell description, Bigby's Hand is an object:
The hand is an object that has AC 20 and hit points equal to your hit point maximum.
As an object, my instinct is to say that like other objects, Bigby's Hand could only be healed by a spell like Mending which explicitly heals objects:
This spell repairs a single break or tear in an object you touch.
However, Mending has 2 obstacles. First is it has a casting time of 1 minute, the same as the duration of the Bigby's Hand spell. So functionally I don't know that the timing could work. Second, Mending continues to say:
This spell can physically repair a magic item or construct, but the spell can't restore magic to such an object.
From RAI this wording might also prevent healing Bigby's Hand since it is a conjured magical object, the healing of which might be considered "restoring magic to the item".
I'm also not aware of any other spells used to heal objects other than Mending.
So the question remains: is there a way to heal Bigby's Hand?