I have been struggling with finding access, by my own means, to the question Heidegger poses in Introduction to Metaphysicsthrough the history of Philosophy. The question is not an innovation of Heidegger's, but is asked, and often answered, in the history of Philosophy.
Leibniz answers the question in what Heidegger calls the Twenty-four Statements, since, he says, there ought to be a ground for the fact that there is something. For Leibniz, it seems for there to be something requires the possibility of bringing possibilities into actuality. Since there are actual things, it is necessary that these possibilities are brought into actuality, and that whatever is the cause (the 'real ground') of this stepping into reality (coming into existence) is also the necessary ground of the fact of actualities. Of course, this ground is none other than God.
Here is an illustration of Leibniz's work here in terms of the elements involved: 1) the actual that is, and which is known; 2) the demand that we account for the actual's being instead of nothing; 3) the possible from which the actual steps into existence; 4) that which is necessary in the face of the fact that the possible does step into existence.
Any of the actual things could just as well have been nothing, and, for Leibniz, many of possibilities did not come to pass. Coming to pass is determined by God on the basis of the most good. (Goodness now is understood in a way mediated first by the fact that something is rather than not, and should be understood in terms of existence, and not our preference.) For something to not come into existence is for it to have contradicted whatever did come to pass, and also not being as good as what did come to pass.
(I must mention, in defense of Leibniz, that it seems highly important to see the choice to place goodness at the root of the decision of what should be is not arbitrary. The highest order decision about what is actual should align with the highest knowledge of it, and so should be knowledge of what is best, and ultimately good. Here, goodness should not be considered in terms of morally good, since it seems ethics is determined by Leibniz at the end of the Twenty-four Statements in terms of coming to understand the goodness of the world, and to situate our minds to not be at odds with the goodness of existence by expecting things out of it that we should not. This means that the way things are opposed to our desires should have a regulative impact on us so that we come to understand the world better and change ourselves to not be at odds with it.)
So something is, in which case it is the most good, or something is not, which is to say it contradicts the good or is less good. What does nothing mean here? Nothing is not the contradictory, or the less good, since these are still possibilities. Nothing must be understood as something else. Things have less reality if they are less likely to come into existence, and so nothing would seem to be a privation, in some degree, of goodness. So nothing here is not a mere not being actual but a privation. If this is the case, then when we look out and see that there are actual things, we can't suppose that it could have been nothing, since nothing is just privation of what is. This may give us some right to understand nothing is another sense, that is, whatever is not actual is nothing.
The dual notion of nothing we have is first, nothing as privation of goodness or contradiction with what is good, and second, nothing as not being actualized. It appears that the second approach to nothing dominates the question Leibniz answers of why there is something rather than nothing. Because he is focused on the second sense of nothing, he can see the actual in opposition to its alternative, and not just different in degree. The dividing line between something and nothing, then, is determined on the basis of there being goodness (which is our highest way of thinking the best and so the highest kind of knowledge we tend towards). But this goodness is decided on the basis of what simply is (which could have still been anything). This establishes a kind of circle that is driven by the pursuit of the highest kind of knowledge for us.
Looking at the four-fold division above, then we can note that (2) the demand that we determine the question is driven by the demand to know the highest, and so the direction of (4) how we determine what is necessary is established in this practical manner (rather than upon an analysis of the 'objectivity of the object', which is an alternative approach).