Is there any conjecture or famous unsolved problem, that doesn't require much prerequisite knowledge and could be plausibly proven / solved by freshman?
My hero is average freshman in mathematics, that proves a famous conjecture by mistaking it for homework, like George Dantzig.
Maybe something in combinatorics if this reddit comment is true
A few years ago at my university the final test on combinatorics included some unsolved problems. The students were supposed to have enough insight to realize which problems were the easy solvable ones and which ones were a waste of time to try to solve.
One of the students (this course is usually taken by first or second year students) actually solved one of the unsolved problems. It wasn't one of the really famous unsolved problems included on the test, but his result was certainly unknown.
The conclusion was somewhat less dramatic, though: the professors thought about his solution for some time (months) and after they were convinced that there isn't a loophole in the argument, the result was published and eventually became the basis for this guy's PhD. research.
Problems in combinatorics are certainly easier to approach on this level, since their solution usually involves some clever trick, rather than extensive application of deep theorems.