Perhaps an easier way to visualize it would be to think of spacetime as a chessboard, with pieces. There are 64 squares to go to, but every piece is limited in its mobility by the moves it is allowed to make, and that's what determines how the game will be played.
For instance, the pawn can only move straight ahead by one square, except on its first move ─ then it can move straight ahead by either one or two squares ─ and when it captures another piece, which is always a diagonal move. Considering that the pawns are aligned on the second rank for white (or the fifth rank for black) at the start of the game, they can never move to the first rank (for white) or the sixth rank (for black). As another example, the bishops are always tied to the color of the square they are on at the start of the game, and so either player has one light-square bishop and one dark-square bishop.
The number of possible legal moves available between both players leads to an astronomical amount of permutations, and yet it is still a finite number due to the limited mobility of each of the pieces and the fact that there are only 64 squares ─ 32 light ones and 32 dark ones. Spacetime ─ space and time combined ─ is like that chessboard.
I'm oversimplifying things here, but you should get the idea.