The attacking player attacks with some creature. The defending player doesn’t block, so the attacking player plays [[Michelangelo, Improviser]] using his first ability (sneak). The defending player targets Michelangelo using a [[Maze of Ith]].
Can the defending player target Michelangelo using the Maze (probably yes, since it enters attacking), and is it possible early enough to prevent it from dealing damage (thus also preventing his second ability from triggering)?


Worth calling out here is the opponent can still sneak/ninjutsu in response if they have another card that can in hand. If you suspect that the opponent plays more than one card with sneak/ninjutsu and has untapped mana, you might want to consider that possibility before targeting the creature.
As an example:
Basically, during the declare blockers step, sneak/ninjutsu lets you juggle creatures around at instant speed as long as you have the mana.