During the setup the players are required to draw 9 cards to infect the starting cities before the game starts. What if for example no red disease card is drawn? Is the red disease already eradicated before we start the game?
No, a disease with no cubes at the beginning of the game is not eradicated.
For a disease to be eradicated, it must be cured in addition to there being no cubes left of its color. At the beginning of the game, it is clearly not cured. If you subsequently draw an infection card for that color, you still add a cube to that city. If you manage to discover the cure before that happens, then it's eradicated.
Various snippets from the rules: