If you gain presence during the turn (after Growth) and uncover the "any" or another element, can you then use it for other powers?

If you gain presence during the turn (after Growth) and uncover the "any" or another element, can you then use it for other powers?

Yes, you can start using elements as soon as you gain them. (p. 14) Similarly, if you are able to play a card mid-turn, you get the effects of its Elements immediately.
(And if some effect were to cover an Element by returning Presence to your track, or destroy a Power card in play, you'd immediately lose access to the elements.)