In most games, it appears after the starter is chosen.
So, for example, when you pick a Shiny Mudkip, it will look blue when you see it by Treecko and Torchic, but will be Purple when it’s sent out to fight Poocheyana. This goes for all games except for HGSS, where you can see the starters in their shiny form before they are picked. This makes shiny hunting starters rather easy in HGSS.
Source:Experience for HGSS, watching lots of videos.