I'm really curious because when you go to catch Zygarde there are their orbs all around the area. When I saw this I thought there might be a chance to get at least one of them without trading. Is it possible?
Nope, you can't get Dialga, Palkia, or Giratina in Pokémon X/Y. The only way to get them would be through an event, and the last event for that trio on X/Y/OR/AS happened back in 2015.
Sources: Events, Legends