key to a solution; first step toward a solution; thread to unravel a mystery
Refers to a clue, hint, or initial breakthrough that leads to solving a problem or mystery. Often used when a difficult situation begins to show a way forward.
After years of research, I finally found a key to the solution.
This data might be the thread to unravel the case.
手がかり is a more general word for a clue or lead, while 解決の糸口 specifically emphasizes the beginning of a solution process.
突破口 means a breakthrough or opening, often used in negotiations or difficult situations, but 解決の糸口 focuses on the initial hint that starts the resolution.
Compound of 解決 (solution) + の (possessive particle) + 糸口 (thread end, clue). The expression metaphorically likens finding a solution to picking up the end of a tangled thread.