The description for Mage Hand lists a casting time of 1 action. The spell's description elaborates on its function as:
You can use your action to control the hand.
I would personally interpret this such that you could only start using your Mage Hand the turn after you cast it. However, this makes it pretty unusable in combat or situations where immediate action is required.
Is my assumption correct that the casting time of one action makes the Mage Hand only controllable the turn after it was cast?