For all we know, this is how everyone actually solves problems all the time, the difference being that when most people are asked how they solved a problem they confabulate something after the fact. If you want to gain this skill, perhaps you could consciously practice coming up with a story for how a solution could have been found after you do it. Maybe look at a book like Polya's How to Solve It and construct a sequence of hints like those in the book ("consider special cases", "solve a simpler problem", etc.) that could conceivably lead a less intuitive person to the answer.