At the end of your first plate appearance or fielding opportunity you will see a "O - Watch Game" button rendered for only a second or two at the bottom right of your screen. If you press the "O" on your controller in time you will be put into the full game mode where you can play every defensive pitch for the rest of the game in the field or play every offensive pitch in the dugout, at the plate or on base. Also, the "O - Watch Game" button is rendered after every pitch. Be careful not the press the "O" button again otherwise you will be taken out of this mode and forced to jump several innings into the future of your game or possibly to the end of the game.
I can't for the life of me figure out why they do not make this available to us at the beginning of the game.