Can Evelyn Entracing be activated in response to a sprite dying in the beginning phase?

Yes, you can activate Evelynn, Entrancing in response to a Sprite dying from the Temporary keyword during your Beginning Phase.

According to FAQ #4120 and FAQ #6422, the Temporary keyword is a triggered ability that is placed on the chain at the start of the Beginning Phase. Because it is on the chain, it creates a window where you can play Reaction speed effects.

As Evelynn, Entrancing has the Hidden keyword—which allows you to play the card from its facedown state—you can use this timing to reveal her in response to the Temporary trigger.

Sequence of Events

1. Beginning Phase: The Temporary ability of your Sprite triggers and is placed on the chain.
2. Reaction: You play your hidden Evelynn, Entrancing in response.
3. Resolution (LIFO - Rule 336.1):
   • Evelynn's "When you play me from face down" triggered ability resolves first.
   • The Temporary trigger resolves, and your Sprite dies.

Note: Per Rule 737.1.d.3, when you play a hidden unit, you must play it at the same battlefield where the spell or permanent was hidden.