For the 256 Pac-Dot run to be accepted, the combo for the dots has to start where the game starts or can it be made in the course of the game?

Rules state time begins when game is started from the main menu. Time ends on the 256 dot. These dots can gotten at any point in the game. The longer it takes the further down on the board you will be but you will be on the board. So the combo can happen anytime in the game though for records it is best to start and end a combo at the beginning of the game it is not required to do so to be on the board.