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What if Midoriya’s quirk is his analysis skills, I mean in the show they comment on his analysis skills a couple times.
And it was revealed that the doctor that diagnosed him was Dr.Ujiko, All for One’s doctor, so what if Ujiko had a pre-scanned x-ray of a quirkless kid’s foot and said it was Midoriya’s.
So what if Dr. Ujiko told Midoriya he was quirkless so All for One could steal his quirk, but All for One never got to him.
So Midoriya has a quirk without realizing it because there is no physical signs of it. Just his analyzing skills.
Another random theory that popped in my head XD