Determining how the first cause is able to exist is a profoundly difficult problem, and rejecting certain "wrong answers" helps to sharpen the discussion.

Firstly, the first cause does not exist by any type of recursion/self-causation. The first cause cannot be said to have "made itself exist". Making oneself exist is as impossible as nothing turning into something, and in fact, the two are identical, because before the first cause existed, it was not there to cause itself to exist.

Secondly, there can be no principle or rule external to the first cause which can explain its existence. If such a principle provided the mechanism by which the first cause existed, it would have "caused" the first cause, which is contradictory, and would only move the problem of existence to the principle. But, if such a principle does not provide a mechanism for the first cause to exist, it does not "explain" it either, because the mechanism by which the first cause exists is one and the same as the "explanation" for how it exists.

Therefore, the kinds of explanations used to explain the existence of everything else cannot be resorted to. In every other circumstance, the existence of something can be explained by examining its cause, which is always separate from and prior to itself. For the first cause, the explanation cannot be found outside of itself, but it also cannot be said to have "caused" itself.

There are two main ways that people have tried to make sense of this. The first is to propose that there is no explanation for why the first cause exists. Instead, it simply exists for no reason. The second family of explanations appeals to some form of argument from necessity - the first cause has a nature such that it cannot fail to exist.

The first type of answer proposes an arbitrary reality. The existence of reality, and the characteristics of it, have no explanation - they are brute facts. Because this answer is somewhat of a non-answer, the investigation stops here. Why this particular reality? No reason. Why should anyone believe that such a thing can exist without reason or explanation? Essentially only because they have examined the alternatives which offer a non-arbitrary foundation, and reject them.

The second type of answer attempts to offer a non-arbitrary answer to why the first cause exists. This position rejects the entire concept of a brute fact. It argues that nothing can have no explanation. Everything - even the first cause - has an explanation. But, since the standard causal explanation is not available to the first cause, they propose that there is something about the first cause which makes it so that it "must" exist, necessarily.

Why "necessarily" instead of just "the first cause happens to exist for a reason, but also could conceivably have not existed"? If the first cause simply "happened" to exist, that would return the foundation to arbitrariness. There would be no particular reason that existence attained instead of not attaining. So, this position uses the "necessary" language very intentionally, to avoid returning to arbitrariness.

How is it possible for something's nature to make its own nonexistence impossible? Some argue along the lines of the Ontological Argument, which argues that the greatest conceivable being has necessary existence as a characteristic, because it is greater to exist in all possible worlds than it is to exist in only some possible worlds.

Finally, note that this question is separate from the question of whether or not God exists. Whether or not the first cause is a brute fact is different from whether or not the first cause is a conscious entity, though the non-arbitrary answers tend toward Theism, because the nature that they defend usually has all "great-making" characteristics, including intellect.