This is untested, but try adding a line of script to the bottom of the game start event (in the all-black map, upper left corner) that reads "pbSafariState.pbStart(999)" or however many Safari Balls you want in their inventory.
You will have to find some way of including "pbSafariState.pbEnd" in an event triggered by the player successfully catching a Pokemon, though. Otherwise the entire game will be in the Safari Zone. My suggestion is have it in a door event that the player can only walk through if they have a Pokemon, otherwise the character thinks to themself I came here for a Pokemon, I can't leave yet.