The PHB would seem to indicate that no, this lets them pass through without provoking opportunity attacks. (The hand is moving between enemies, not trying to shove them.)
From the description of opportunity attacks (PHB, p. 195):
You also don't provoke an opportunity attack when you teleport or when
someone or something moves you without using your movement, action, or
Does this let someone rescue an unconscious ally by using Bigby's hand to carry them across the battlefield back to the cleric for healing without provoking attacks of opportunity, for example?