My first shiny was Rattata @ Lv. 3. Yup, an early game shiny! And ya know what? I couldn't catch it because I didn't have any Pokeballs. I literally stared at my GBA SP screen for 5 minutes before shutting the dang thing off in frustration. Sometime after I surprisingly found another shiny Rattata @ Lv. 3 (or 4) early on, however, this time I had Pokeballs and...
... caught it! That was a long time ago, though.