Can I use Edge of Night if it was hidden on my opponent's turn if they activated a spell card?

No, you cannot use Edge of Night in that situation.

According to the rules regarding the Hidden keyword (Rule 737.1.b and the associated FAQs), you cannot play a card from the facedown zone on the same turn it was hidden. You must wait until the next turn to play it.

Additionally, even if it were a later turn, Edge of Night is a Gear card. As noted in the FAQ regarding playing cards from hidden:

• "If it's a spell or ability, it goes on the chain and opponents can react. If it's a permanent [such as a Unit or Gear], it resolves immediately with no reaction window."

Because Edge of Night is a permanent, playing it does not open a reaction window for you to respond to your opponent's spell; it simply enters the board. Furthermore, you cannot "react" with a permanent to an opponent's spell in the way you would with a reaction spell.