Carol Danvers – damsel in distress: Captain Marvel #1 – May, 1968
Captain Marvel received his own comic book after Marvel-Super-Heroes #12-13. The story picks up exactly where Marvel-Super-Heroes #13 stopped, with Captain Mar-Vell fighting against the Intergalactic Sentry #459. The character of Carol Danvers is now a side character in Captain Mar-Vell's solo comic book.
During the fight between Mar-Vell and the Sentry, Carol gets closer to get a better look at Mar-Vell. Not a smart move as we later see her claiming out of debris that fell because of the fight.
And Danvers becomes a classic damsel in distress. She's stands too close to Mar-Vell who is being attacked by the Sentry. Meaning he has to save her and himself.
Captain Mar-Vell tells Danvers that resistance is the only way to survive. In response she thinks that "I almost believe -- that we have a chance. Of survival!" Even though she has no idea who he is, and have never seen him use his powers. For her he's a man in a costume who appears to be strong and authoritative so she automatically believes in him. But then again, it is a world in which superhero exists.
When Captain Mar-Vell tries to attack the Sentry again, it doesn't work, and Carol yells that it isn't working. In response the Sentry calls Danvers a "whimpering female". Which is not insulting at all. Captain Mar-Vell adds to this insult when he and Carol start to run away from the robot and he tells her: "keep moving girl!". Female, girl, all words to avoid calling her a woman, a grown up.
Eventually Mar-Vell defeats the Sentry. He tells Danvers to runaway before the robot explodes, and she refuses. But there is nothing to fear as Captain Mar-Vell manages to save Carol Danvers.
Mar-Vell carries her unconscious body safely away, a classic damsel in distress imagery. After Carol wakes up she states that she doesn't remember what happened, that she must be in shock; which is possible after this near death experience. She asks Mar-Vell to stay, but he has to leave.
Carol wants to know more about Mar-Vell and the expression on her face shows more than just professional curiosity.
Suddenly in this issue Carol Danvers isn't so smart. She comes too close to danger and almost pays with her life, but is saved by Mar-Vell. From a capable chief of security, she becomes the damsel in distress in the Captain Mar-Vell story, completed with first signs of infatuation.
However, there is a different perspective available, and you can choose your favorite interpretation. The soldiers on the base tried to fight the Sentry themselves and nearly died doing so. They tried to buy Mar-Vell some time and failed. Danvers is just a human caught in an inhuman situation and Mar-Vell saved her as he has save everyone else. We all suffer from a mild case of super-hero worship similarly to Danvers, that's why we love reading comic books.