‘A golden key opens any door’ is the opinion that sufficient money, or the promise of it, will allow the possessor of it to do anything they wish.

This notion must be as old as money itself. The first person who is known to have written it down is the English playwright John Lyly, in Euphues and his England, 1580:

Who is so ignorant that knoweth not, gold be a key for euery locke, chieflye with his Ladye.