Does Awakening of Vitu-Ghazi trigger the ability of Kiora, Behemoth Beckoner?
It doesn't trigger.



It's not simply a question of checking if the state of the game went from not having a creature of power 4 or greater on the battlefield to having one.

An object only enters the battlefield when it moves from a zone other than the battlefield (e.g. hand, graveyard, exile) to the battlefield or when it's otherwise created on the battlefield.


  Enters the Battlefield
  A nontoken permanent “enters the battlefield” when it’s moved onto the battlefield from another zone. A token “enters the battlefield” when it’s created. See rules 403.3, 603.6a, 603.6d, and 614.12.


Since the land in question already existed, and since the land in question was already on the battlefield, no object entered the battlefield (much less one that was a creature with power 4 or greater). As such, the ability isn't triggered.

A ruling on Kiora, Behemoth Beckoner reminds you of this:


  However, you can’t have a creature with power 3 or less enter the battlefield, raise its power with a spell, an activated ability, or a triggered ability, and have Kiora’s ability trigger.