Of course!
Well, you start the game when the first timer hits 0. Then, as the second timer is counting down, select "New Game", name your character, etc. Then, get to the screen where Professor Oak says "See you later!", but don't press A yet.
Wait until the second timer hits 0, then press A. Your ID/SID is generated right when you press A on the second timer.
Chances are, you won't hit your ID/SID on the first try, but that's why you keep trying to see how close you were! :)