I'm not entirely sure if this character qualifies or not - if he doesn't, I'll change my nomination.
Hawkeye (Clint Barton)
Unlike the MCU version, Clint Barton didn't start out as a globe-trotting super-spy - instead, he was a carny who saw Iron Man fly by, noticed that the superhero got a ton of attention, and thought "Psh - I can do that!" He dressed in a garish costume and set out to foil a bank robbery, only for him to be mistaken for one of the robbers and brought into conflict with Iron Man.
Shortly afterwards, he joined the Avengers, where he became one of their major recurring members, and went from the arrogant newcomer to the leader of the team's west coast division. This is probably the main reason why I'm not sure if he qualifies (the Avengers are generally seen as the "ivory tower" or the elites of superheroes, cut off from the average citizen and their struggles), but Matt Fraction's Hawkeye series reinvented Clint as a street level hero when he's not with the Avengers, fighting Russian gangsters who pepper their sentences with "bro" and generally trying to keep his neighbourhood safe.
(as a side note, I debated which Hawkeye to include, since Kate Bishop could also be interesting, but if I could only pick one, I felt like I should pick Clint)
Unlike the other Avengers, Hawkeye doesn't have high-tech armour, a super soldier serum, godly powers, or any kind of superpowers whatsoever - just a bow and a series of trick arrows, such as the boomerang arrow, sonic arrow, or smoke bomb arrow.