Pieces don't fall together. Somebody sits at the table trying the wrong ones for an hour, and the click at the end is preceded by a great deal of unglamorous fitting.
The passive voice is the problem in this idea. It suggests waiting, and that waiting is a strategy.
Some things do resolve on their own. More of them resolve because a person kept picking up pieces and testing them against edges. Handle one piece today — the loose end you have been leaving loose. Perfect timing usually describes, after the fact, effort that nobody saw.