Nope, there is such thing as quirkless people, but the population of quirkless people is decreasing and there's a benefit of being quirkless before one for all but I'm afraid I might be spoiling the manga for you
MAYBE EVERYONE HAS A QUIRK, IT’S JUST THAT A LOT MORE PEOPLE HAVE QUIRKS INVOLVING INGESTING BLOOD, LIKE STAIN OR TOGA, JUST HAVEN’T EVER ACTUALLY DRANK BLOOD