I don't view "Hero" as a power level. Rather, it's a role open to anyone at any power level, and not one that all characters inevitably embrace.
That said, I don't think that D&D has ever, as a system, put forward the idea that 1st level characters are just Average Joe. I'm quite certain many people have chosen to play it that way, perhaps even from the earliest days of the game, but they're working somewhat against the system's assumptions rather than with them. The system has, as far as I can see, always assumed you're already at least somewhat ahead of the pack, unless you assume a world in which all people have a class (are all tavern wenches Fighting Women?).
The Fighting Man was explicitly a Veteran at first level. He'd already seen combat, already mastered the use of dozens of weapons and the best armour. He's not the farmhand who's never held a sword before, thrust into the midst of unexpected adventure and surviving by the skin of his teeth.
Joe Average, last I checked, cannot cast any spells per day, not even the paltry one per day of a first level Magic User. You're not the sorcerer's apprentice on his first day, here.
A priest, even one without training in armour and the ability to call upon divine magic, generally has to train for years in order to be ordained. The Cleric is not the altar boy.
Later versions of the system are even more explicit in this above-ordinariness. If the average ability score is 10/11, then a system that encourages you to use 4d6 (drop lowest) to generate ability scores (mean outcome: 13) is telling you right from the start that you're above average. Nevermind that there's a specific Commoner class: anyone who starts elsewhere clearly is not the common man.
4E never made any bones about it: the system simply assumes you're already an adventurer (or "heroic adventurer", as they phrase it). When thinking about your character's background, you're encouraged to answer the question "Why did you decide to become an adventurer?", treating the fact that you did so as a fait accompli before your character even sees play at the table. It then backs this up mechanically by ensuring that your first level character is robust enough and knows enough combat techniques that you can go four or five rounds of combat without repeating yourself once. A fighter who can control his opponent's movements at-will is clearly not a greenhorn. A wizard who can do magic at-will isn't wet behind the ears. A cleric who can successfully call upon their god to bestow healing twice every five minutes has obviously gone a little beyond his first prayer-meeting.
