Is he perhaps waiting on the “divinity who shapes our ends” to provide the opportunity? Or is it simply not in him to be an agent of vengeance, the stereotypical avenging role Laertes is so manifestly comfortable with (to Hamlet's disgust)? It is noteworthy that when called upon by the Ghost to take vengeance he instead (a) writes and directs a play and (b) serves as his mother's ad hoc priest/confessor. Theatrical impresarios and priests alike work behind the scenes, pulling strings, directing and ordering others: they take no public action of their own.
But what if that's God's job? It's interesting that everyone in the end pays for their sins without Hamlet's planning or deciding to make them do so. There's a divinity that shapes their ends too. So if the play begins by bringing in a Purgatorial ghost whose existence suggests that “there are more things in heaven and earth than are dreamt of in [Horatio's Lutheran] philosophy,” it ends with what seems to be an affirmation of a key principle of the magisterial Reformation: the meticulous providence of God.
In short, the evidence in this play for life's meaning and purpose points in multiple directions — as does all evidence for what human beings are like. Thus Hamlet's words to Rosencrantz and Guildernstern:
I have of late — but wherefore I know not — lost all my mirth, forgone all custom of exercises, and indeed it goes so heavily with my disposition that this goodly frame, the earth, seems to me a sterile promontory; this most excellent canopy, the air — look you, this brave o'erhanging firmament, this majestical roof fretted with golden fire — why, it appears no other thing to me than a foul and pestilent congregation of vapors. What a piece of work is a man! How noble in reason, how infinite in faculty! In form and moving how express and admirable! In action how like an angel, in apprehension how like a god! The beauty of the world. The paragon of animals. And yet, to me, what is this quintessence of dust?
So this is indeed “a play in the interrogative mood” (as Harry Levin write long ago in a still-incisive book) and it seems determined to dramatize our questions rather than offer us any answers to them. In this sense it is very much a document of its time. Not for this period the bold attempt by Thomas Aquinas to sort out and systematize virtually the whole of human knowledge; there was already too much to know, and no one capable of ordering it all. Instead the watchword is, and had to be, Montaigne's questioning motto, Que scay-je? What do I know?
Long ago Northrop Frye wrote that if Hamlet was the definitive Shakespearean play of the nineteenth century, and King Lear, with its mixture of tragedy and absurdity, of the twentieth, the play for the twenty-first century might well be Antony and Cleopatra. Why? Because, Frye argued, it is about how deeply personal relations are usurped by world-historical events. That seemed plausible at the time, but maybe, as it turns out, we're back in the world of Hamlet: confronted constantly by evidence of what we know, what we're capable of, and at the same time faced with what we can't master and can't understand. We look into the ever-more-technologically-sophisticated future and we can't tell whether it points to the apotheosis of humanity or its utter abrogation, and we're not even sure we know how we might tell the difference. We may all be Hamlets — “reduplicated Hamlets,” in Auden's phrase — after all. What do we know?