Sneak timing and Maze of Ith

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)?