Throughout Sophocles' Oedipus the King, the playwright gives the audience several glimpses and recollections that Oedipus has, indeed, killed his father and married his mother.
Early in the play, before Teiresias arrives, Creon recalls for Oedipus what he knows about the death of Laius. Oedipus learns from Creon that Laius' death was murdered, that Laius was on his way to Delphi when it happened, and that only one person from Laius' entourage escaped death. According to that person, however, Laius and company were attacked by multiple robbers and not one person.
Also, before Teiresias arrives, Oedipus questions the old men of Thebes (i.e., the Chorus) about Laius' death. They also report that "Laius was killed by certain travellers" (Ian Johnston translation).
Later, when Oedipus accuses Creon of conspiring against him, Creon reveals that it has been many years since Laius' murder occurred, thus providing another clue that would link Oedipus to the crime.
When Jocasta comes on stage to calm the dispute between Creon and Oedipus, she provides further information about Laius' death. Jocasta's information about the murder occurring "at a place where three roads meet" provides an additional detail that causes Oedipus to become quite worried. Furthermore, she specifies that the murder occurred just before Oedipus became king of Thebes. She also adds additional detail about the number of men Laius had with him at the time of his death.
After Oedipus hears Jocasta's account of Laius' death, he recalls his own bloody encounter with a man and his entourage at "a spot where three roads meet". Still, Oedipus is not completely certain that he was Laius' killer because of the persistent report that Laius was killed by multiple persons and not one solitary person.
So, other than the comments by Teiresias and prior to the arrival of the two shepherds, Sophocles provides the audience with plenty of indications that Oedipus is Laius' killer. In fact, it appears that each person that comes on stage with Oedipus provides him with some bit of information about Laius' death. Oedipus' only stumbling block to piecing together the mystery is the account that Laius was killed by multiple attackers.