I find this a difficult question to answer within the framework of anything resembling an objective, universal truth so I don't know if anyone's answers (let alone my own) will achieve any solid end here. Nonetheless, let us try. The question is asking how the PCs are represented in the fiction at 1st level and how they are recognized, as a result of this representation, by their fictional contemporaries - NPCs.
How do we make this determination?
XPs?
Nope. XP does not correlate to "a metric that properly encompasses a persons experience". It is entirely a meta-game construct; a pacing mechanism for PC potency versus adventure content. If NPCs stuck around a PC for a long enough period of time (eg - over multiple levels), they would then see the impact of XP and would be able to reliably confirm that this guy's XP is greater than that guy's XP. But just a guy walking down the street? Nope.
HPs?
Nope. HPs do not correlate to size, density, meatiness, hardness or anything "real world". It, like XP, is entirely a meta-game construct; a pacing mechanism for PC survivability (plot protection primarily) versus adventure content. If NPCs stuck around a PC for a long enough period of time (eg - over multiple levels), they would then see the impact of HPs and would be able to reliably confirm that this guy's HP is greater than that guy's HP. But just a guy walking down the street? Nope.
Class Features?
Hmmm...maybe. In 5th edition terms, most NPCs likely have little more than a Background. That leaves Class Features and Specialties (and the inevitable pre-game stories/training/legacy that produced them and culled these people from the common rabble). That clearly sets them apart. This is where acumen reliably reproduces proficiency. You could demonstrate over and over that you are a swordsman set apart from the rest (Proficiency bonus, At-Wills, BAB, THAC0, Damage Bonus, Combat Superiority, etc). You could display your "cut-above the rest" ability to locate trail signs, tracks, natural hazards, safe havens. You could Prestidigitate, Mage Hand, At-Will Attack Power, etc. You could lay your hands on a townsperson's head laceration (specifically in a locale bereft of any clergy) and it may disappear. Etc, etc.
Ability Scores?
This is a product of world-building so there will be some incongruency here (table to table and system to system). A commoner's Ability Scores might be a standard array outside of point buy. This approach would clearly display the relative impotency of the commoner versus the adventurer. However, some folks may determine that they should roll for their commoner's or point buy (relevant folks) just like PCs. In 4e, the Servant (which would effectively be the equivalent of commoner) is 10 across the board except for one 8. The Thug is 14, 10, 12, 9, 10, 11. In Pathfinder, the Farmer is 11, 10, 12, 13, 10, 9. I would say, RAW, these are both very good representatives of the "lay class" of the various D&D civilization. As such, Ability Scores would clearly set a 1st level adventurer apart from the common man. They would almost assuredly be beyond the physical scope of the common man in almost all ability scores (in some cases dramatically so) either through genetics or training regime (or both). Nonetheless, the disparity would be clear and present to your standard commoner. They would take notice and it would be inescapable.
Stories and immediate travails?
Yes. There are so many editions that its difficult to go through all of them. However, taken together, they (yes, even 4e) have an expectation of PC:adventure content that scales with acute congruency. So what are their stories at 1st level? They're routing a band of marauding goblins that are raiding the local village. They are protecting a merchant's caravan that has been repeatedly ambushed (goods confiscated, guards killed or captured) by a notorious band of highwaymen. There is plenty more where that came from. If I was an NPC (specifically a young child) I would look upon those figures with the awe reserved for a hero (much like we look upon the men who stormed the Beaches on D-Day).
I think, for an everyday NPC, a 1st level PC's acumen (class features/build resources beyond background), Ability Scores, and the pre-game story/legacy/training that culled them from their peers + the 1st level stories that they immediately produce would be impossible to deny. They would clearly set them apart from "every-man."