As alluded to in other comments and answers, I think part of the confusion here (and often in similar inquiries) is due to the notion that there is a well-defined "problem" that is either "solved" or not. Sure, there are "long-standing unresolved" very-specific questions that may admit yes-or-no answers, but, even then, in real life one makes partial progress on things. It's not all-or-nothing.
For that matter, often a very meaningful project can amount to "try to understand X better"... where X is a thing worth understanding better. Very amorphous, really. Such situations are exactly where an experienced person can have good hunches about incremental progress, and also be able to appraise the significance of various incremental advances.
This is why most theses, and most research projects viewed "in the small", do not have an easily-describable, easily-motivated goal. Indeed, in some cases the acquisition of sufficient technical savvy to understand the short-term goal is a project in itself, and it is often the case that "understanding the question" is sufficient to nearly have an answer.
From another angle: it can happen that a project is very plausibly feasible, but the execution of it would require considerable exertion. That is, the thing does not magically do itself. And one never knows with certainty what unexpected intermediate tasks may arise.