We'll admit that The Flies isn't exactly a classic quest tale. So if you want to try and fit it to the classic quest plot, you've got to take some liberties. The "journey" that Orestes takes brings him from his home to the land of Argos – both his decision to travel (the call) and the traveling itself happen before the play begins. The action begins with his arrival in Argos.
This happens before we join the action.
His people are miserable and mentally enslaved. The gods are unjust and obsessed with keeping the mortals miserable. His mother's sleeping with the enemy and his sister is a maid in her own palace. Orestes is not a happy camper.
This is where the hero is tested and forced to prove himself. For Orestes, these are ideological tests, and he passes them at the end of Act II, Scene i when he resolves to choose his own path and take the burden of freedom heavily upon his shoulders.
Orestes's "thrilling escape" isn't from death so much as it is from bad faith. He escapes from self-deception, passivity, and being-for-others. He experiences a sense of renewal and even re-birth, which he describes in detail in the play's third act.