Can Pokémon be shiny from the start of the game?

Hello, I just started my first playthrough of Black and plan on doing a Shiny only playthrough. I just chose my starter and I’m currently hunting on route 2 just after getting the running shoes. My question is: can you get shiny pokemon at this time? I’ve played older and newer games and the answer has always been yes but I’m very anxious about stuff like this and don’t want to waste a bunch of my time. Any answers would be greatly appreciated, thanks!

Edit: I got my Shiny Purrloin after 1,384 encounters! :)