Learn English – Word for “valid excuse”

You are right that ignorant/ignorance often carries a negative sense ("He's so ignorant!"), but it can also be used neutrally ("Ignorant of what had happened in my absence, I continued as before"). It can certainly be used to express humility ("Forgive my ignorance, but who is the current president of South Korea?").

For the neutral sense there is also unaware (and unawareness).

There are not many emphatically positive expressions for lack of knowledge, since this is usually considered a negative (though you might argue innocent has this sense; also ignorant and unaware are often combined with blissfully, after the proverb Ignorance is bliss). But there are expressions for situations where lack of knowledge is expected, and therefore perhaps less negative — for instance, novice, apprentice, learner, beginner, and if your aim is to express humility then any of these would be appropriate.

I think if used in the context you've described curious will consistently have a positive connotation; I can't conceive of how curiosity about an academic subject could be taken negatively.

Perhaps the word 'interested' is less likely to be construed negatively. "She was interested in biology".

I think that any negative connotation attached to any word that describes inquisitiveness stems from the human desire for privacy; there will always be certain subjects that people don't want examined, as such there will always be the potential for any type of inquisitiveness to be spun negatively.