The German usage of Gretchenfrage may preserve something of its original weight in Goethe’s Faust, say, concerning some fundamental question of human existence or society, or it may have become so semantically lightened that it may designate any question a writer wishes to describe as difficult or important:
Gretchenfrage: Lassen sich effiziente Marketingkampagnen tatsächlich planen?
Vital question: Can efficient marketing campaigns actually be planned? — Harald Reil, “Erfolgskontrolle”, GENIOS WirtschaftsWissen Nr. 04, 10.04.2013.
While it might be amusing to substitute this question for Goethe’s original,this quite mercantile version does point out the difficulty of your question. An English equivalent needs to determine which of the many aspects of the German expression are at play in a given context. For instance, I chose vital to suggest the importance the writer wishes to convey, even though the question here is merely a rhetorical one.
If a Gretchenfrage is one that penetrates to the heart of the matter, then it can be called a crucial question:
Yet the crucial question to which this general conception gives rise is the epistemic one raised by Berkeley and Kant: if all that is ever given in experience is ideas, and reality is not an idea or a relation among ideas, how can we ever know whether our ideas correspond with reality? — G. Soffer, Husserl and the Question of Relativism, 2012, 60.
Here is the crucial question. From a practical point of view, society must have some way of protecting itself and its members against abuses committed in the name of the free exercise of religion. And it is the function of the state to provide this protection. — John Courtney Murray, J. Leon Hooper, Religious Liberty: Catholic Struggles with Pluralism, 1993, 151.
Or perhaps pivotal:
Yet we might also say that some ancient Greek philosophers already asked the pivotal question. In The Laws, Plato seeks to demonstrate the existence of the gods with the argument from design: “Why, to begin with, think of the earth, and sun, and planets, and everything! …” — William Sims Bainbridge, Virtual Sociocultural Convergence, 2016, 233.
In informal contexts, this expression and its inflated permutations are quite common:
For a lifetime, my father, when presented with a deep question, probably from a child's mind, would respond, “well, that's a 64 dollar question”. — Hugh Mann, Spiritfarmer Aftermath, 2013.
As the German expression, a $64 question preserves a cultural reference, though hardly belletristic: this amount was the highest prize awarded on a popular radio quiz show in the 1940s; its revival on modern television raised the amount to $64,000, and virtually any large amount of money can substitute.
Since there is no single German Gretchenfrage beyond Goethe’s original, there can be no single English equivalent. Any adjective of impotance, urgency, complexity, or incisiveness can modify question depending on which quality a writer has in mind.