In Sophocles' Oedipus the King, Oedipus is not the only person to have visited Apollo's oracle at Delphi.
Chronologically speaking, Oedipus' father was on a trip to Delphi when he was killed, ironically by his own son Oedipus (see lines 113 and 734). Likewise, Oedipus himself was on his way to Delphi to try to discover the identity of his true parents. So, it appears Laius and Oedipus were both on trips to and/or from Apollo's oracle when their fateful encounter took place.
As Sophocles' play opens, Creon also has made a pilgrimage to Delphi to discover what the Thebans should do about the pollution afflicting their city, a pollution caused by their harboring of the killer of Laius. Creon has made this journey because Oedipus sent him "to Pythian Apollo’s shrine" (70; Ian Johnston translation).