Can the Call to Adventure ever come first? I'm drawing a blank on any examples other than my own storyline, but could it still be a satisfying story and character arc if the inciting incident happens within the first few minutes/pages and then proceed to revisit the Old World (not with flashbacks, but in pursuit of his goal and in learning the stakes) on the way to the New World? Or would learning the stakes be the Call to Adventure?

First off, these are not rules, this is not a paint by numbers paradigm. If a writer uses a formula, they will more than likely end up with a formulaic story. This is one reason why I prefer the meta view of the Hero's Journey rather than Campbell's 17 or Voglers distilled 12 stage versions. Not that there is anything inherently wrong with those iterations, rather it's what writers DO with them, desperate to find a formula. That is NOT what Campbell intended, nor Vogler for that matter. Rather the 'stages' are potential narrative elements that we see recurring in stories. That said, I feel entirely comfortable with this meta view as it goes back to Aristotle "Poetics" [Beginning, Middle, End] and frankly it's hard to imagine one telling a story, or anything that people would recognize as a story without these five movements. So to your specific question, in theory you can do anything. Take nonlinear, for example. (500) Days of Summer begins toward the very end of the chronology of Tom and Summer's relationship -- when they meet on the park bench and she conveys what was behind her decision to get married. We only see them sitting together, holding hands, a wedding ring on her finger. Then go back in time. Could you start with a Herald's call? Then go back in time to set up the Protagonist and their Ordinary World? Sure! Would it work? Who knows? Why not try it and see? Or could the P receive a Call To Adventure as the opening scene, only NOT realize it IS the Call until several scenes later? Probably. Would it work? What the hell, give it a shot! The larger point is Separation only means something if we have a sense about the world from which the Protagonist is departing. We need that to provide a context, and thereby understand its significance. Also, too, it is important in highlighting what the P experiences in the New World (Initiation), how it has meaning and impacts him/her. Finally it is important in terms of Return for many reasons, not the least of which is it demonstrates how the P has changed.