In this story, the inciting incident, refusal of the call, and start of the quest are all backstory.
Are you sure? You say they are heroes. They have set out on a secret mission. But is that a departure from their normal world? Or is that what these heros do for a living. Perhaps going on secret missions while posing as cowboys is the normal life for these characters, which is why it seems right to you to start your story there. Maybe it is the thing that happens next that makes them say, Oh oh! This is not an ordinary secret mission disguised as cattle drive. Something is different this time.
The inciting incident of a story is the thing that sets the protagonist on a course for a conflict of values which, in the mirror moment, in the inmost cave, they are finally going to have to face and make a great life-altering decision. The inciting incident, the call to adventure, matters because it prefigures that great life-altering decision. We need it because we need to know what is a stake -- what values are in the balance.
But that moment does not necessarily correspond with the start of the the protagonist's journey. Taking the journey may be very much a normal world thing for the protagonist -- not something that prefigures a great life-altering decision. Those moments can also happen in the middle of a journey. The inciting incident in the life of St. Paul did not happen in Jerusalem but on the road to Damascus.
I'm not saying that a story can't start after the call to adventure, the refusal of the call, and the crossing of the first threshold, though those things will need to be filled in if it does. But don't assume either that a story that begins in the middle of a journey must be beginning after the crossing of the threshold. That event might still be down the road.