OK good! I have a non shiny lvl 1 giritina I got in Heartgold! you have to take a movie or TRU arceus to the sinoh ruins and it unlocks an event where you can pick a Dialga, Palkia or Giritina all lvl 1. I also have a lvl 1 Dialga (sinoh ruins) i got off the GTS.
It's impossible find a Lvl 1 Giratina, since it's legendary. Manaphy comes in an egg @ Lvl 1 but Giratina is suppose to come at 40 or 60 I think... It's modified, I checked... all it says is "Met at lvl 1"