I think we all pretty much want to see the original Captain America and his origin, but considering most of us were introduced to Cap when he was found floating in an ice chunk (by the early Avengers) I think that's how the movie should start. Only not with Avengers/superheroes.
He is found by a Navy carrier and brought aboard where his military I.D. scrambles top brass to the ship, top security. One or more of the brass know who Captain America is/was, as they were teenage soldiers who saw him in action/service. That's when the flashback to his origin begins and the story of his legend gets told. As the story unfolds, you get back and forth cuts from the flashback story to the present showing the ice melting.
Eventually, after the origin (being recounted between the brass, because he is still classified) and a number of kick-butt action war scenes, the story of his disapperance is told, bringing us to the present, by which time a lot of ice has been melted off of him. They are all standing around him remembering what this man meant to them then. One of them says there'll never be another one like him. That's when his eyes open and they all stop dead in their tracks, staring at him. "Call the President!"
Something like that.