We can't know for sure but I am of the belief that arbiters grounds was likely already in existence during OOT. The problem with Hyrule as represented in the games is that it's not consistent in size or geography due to technical limitations of the consoles and because of the time it would take...
Ganondorf was captured and killed by the sages probably very soon after Link returned to the child timeline. Young link would not have been able to kill Ganondorf by himself in his child form and wasn't going to murder the sages prisoner either. He had no idea that Ganondorf would receive the...