Oh yea, it's settled. First time in these boards?
Anyway, that's reads like an origin story to me. That doesn't mean it's her first appearance.
If it came out a week before Captain Marvel #1, and Carol Danvers goes by Captain Marvel in the story, that means it appeared first correct? Appeared first in shops for people to read and buy. Thus, by the truest sense of the word, the first appearance of Carol Danvers as Captain Marvel. I've already made it clear, as does the text in the issue that chronologically it takes place after CM #1, if that's the point you're trying to make.