Can I start with my identity card unrezzed?
At the very start of the Setup section the rules read:


  
  Choose Sides: The players decide who will play as the  Runner and who will play as the Corporation. Then, each  player places his
  identity card faceup in his play area and  takes a corresponding deck.
  


Initial identities go face up.  It's only subsequently that Corporation cards should be installed facedown.

"Rezzing" is furthermore defined as "the act of flipping a facedown card faceup"; so if the initial identities are faceup, there can be no question of them starting the game "unrezzed" (if that wasn't already obvious).