Can I use Diancie's "Sparkling Wish" attack to evolve a Pokemon that I just put into play this turn?
Yes, you can do that.
Sparkling Wish



x2
-20
Sparkling WishSearch your deck for a card that evolves from 1 of your Pokémon and put it onto that Pokémon to evolve it. Then, shuffle your deck.

Diamond StormHeal 30 damage from each of your Fairy Pokémon.
A sudden transformation of Carbink, its pink, glimmering body is said to be the loveliest sight in the whole world.
Can I use Diancie's "Sparkling Wish" attack to evolve a Pokemon that I just put into play this turn?
Yes, you can do that.