In the beginning of the game, your town friend teaches you how capture wild Pokemon. Can those Pokemon be shiny?
Yes they can.
It is possible for the Minccino that appears in the "world of Pokémon" intro in Pokémon Black and White to be Shiny. It is possible for rental Pokémon found in the Battle Factory to be Shiny. It is also possible for the Pokémon that the old man encounters in FireRed and LeafGreen to be Shiny. In Pokémon Ruby, Sapphire, and Emerald, it is possible for the Ralts that Wally catches and the Poochyena/Zigzagoon that attacks Professor Birch to be Shiny.