bchan182 is right! The structural requirements of a Greek Tragedy compel Sophocles to focus on Oedipus' downfall. And yet, there is a more general reason that the play opens with Oedipus having reached the end of his rope in watching the people of Thebes suffer through the plague. He is sure that someone/ some event is responsible for this curse upon his people and he is determined to find out what he/it is. This is the inciting incident of the play, and all drama should begin with this moment of instigation.
An interesting approach that Sophocles takes in this play is that he, of necessity, withholds some of the exposition (background to the opening scene of the play) -- and you mention these events in your question. The reason that Oedipus Rex does not supply the audience all the exposition (as a play might usually do) in the opening scenes is that these events must be discovered by Oedipus, since he does not know or understand the significance of them, as would commonly be true for a protagonist and his own personal history.
eNotes actually has a nice clear diagram of the required rising action of a dramatic text, and you'll find just below the link to the "dramatic structure" page. I've also provided some links to more information about the play and the opening scenes.