Math and Chess - Has Every Game Been Played?

Been playing chess with oldest cub this past week. He has mental limitations, and insists on making the exact same initial moves (pawns altering forward one, forward two) at the beginning of every game.

It just got me to thinking... Mathmatically, given the number of squares on the board, play pieces used, and the moves each one can make, has every game already been played theoretically?

How many games would be needed in order to play all of the possibilities?