It's an interesting question, because fate is such a major theme in the Ancient Greek mythological tradition. Indeed, in some cases, even the gods seem to be subordinate to the power of fate. With that in mind, in discussing Ancient Greek tragedy and myth, I think the subject of fate must always be accounted for, because fate itself is such a critical theme within the entirety of Ancient Greek mythology and epic storytelling.
That being said, I don't think fate plays as central a role in Antigone as it does in stories such as the myth of Oedipus. In that case, the storyline is actively shaped by prophesy, with attempts to supplant fate ultimately resulting in fate's fulfillment.This first happens when Oedipus was abandoned to die, and later when he relocates to Thebes.
Antigone is different, however, in that its characters exhibit far more agency in shaping their particular tragedies. In this case, the tragedy emerges out of a conflict between Antigone and Creon. Antigone defies Creon's law, making a stand for principle and drawing Creon's wrath in the process. She is aware that Creon has forbidden her from burying her brother, but she does so anyway in defense of traditional piety and the rites due to the deceased.
Similarly, Creon chooses to assert his political authority, sentencing her to death rather than showing mercy though he will later change his mind, but only when it is too late. In this case, the tragedy is shaped by this clash of personalities, and the choices these characters have made.