Can I hide Edge of Night while it's on the board?

No, you cannot hide Edge of Night while it is already on the board.

According to the rules for the Hidden keyword (Rule 811.1.b), hiding is a discretionary action that allows you to take a card from your hand or Champion Zone and place it facedown at a battlefield you control. Once a card is already on the board (face up), it is no longer in a zone from which the "Hide" action can be performed.