Can a disease be eradicated at the beginning of 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:


  If the last cube of a cured disease is removed from the board, this disease 
  is eradicated.
  
  [when discovering a cure] If no cubes of this color are on the board, this disease is now eradicated.
  
  To infect a city, place 1 disease cube matching its color onto the city, unless this disease has been eradicated.