The spell description for Bigby's hand on PHB p. 218 (listed as arcane hand in the SRD) states:
The hand is an object that has AC 20 and hit points equal to your hit point maximum. If it drops to 0 hit points, the spell ends. It has a Strength of 26 (+8) and a Dexterity of 10 (+0). The hand doesn't fill its space.
PHB p. 185 and the basic rules state the following regarding interacting with objects:
Objects are immune to poison and psychic damage, but otherwise can be affected by physical and magical attacks much like creatures can. […] Objects always fail Strength and Dexterity saving throws, and they are immune to effects that require other saves.
DMG p. 247 and the DM's basic rules state the following regarding objects:
Objects are immune to poison and psychic damage.
(There is no mention of auto-failing Strength and Dexterity saves in this section.)
As written, Bigby's hand appears to deviate from other types of objects as it has both a Strength and Dexterity score, which seems to suggest it can attempt and succeed at those associated saves, though this would contradict the PHB's statement regarding objects.
As an object, can Bigby's hand attempt and succeed at Strength and Dexterity saving throws?
Best Answer
Bigby's hand always fails Str and Dex saving throws
Objects always fail.
Assigning stats does not specify that an object can make saving throws. It is not a more specific statement that would then follow the specific beats general pattern.
Narrating Saving Throw Mechanic
Bigby's hand and other objects with stats could be narrated as not having the situational awareness nor independence of movement required to attempt to dodge, duck, dive, dip, or dodge.
Animate objects as a counter-example
An example of a spell that creates objects with saving throws, is animate objects. It not only assigns stats, but also explicitly states that the animated objects are creatures.