I think there is an analogy between the question of whether God (or some “first cause”) exists and the question of whether the there was a (remote) past. Consider for a moment Bertrand Russell’s Five Minute Hypothesis: The universe sprang into existence five minutes ago, complete with fossils, false memories, and in general all the supposed “records of the past” intact. As far as our current evidence is concerned, we have no means of distinguishing this scenario from the far more commonly believed one, where the universe is much older; about fifteen billion years, according to modern cosmology. If Russell is correct in supposing his hypothesis to be metaphysically possible, then it seems at first sight that the postulation of remotely past events is superfluous, just as God is supposed by many to be. A common reply to cosmological arguments is to suggest that if we can terminate the regress of causes with God, there is no reason we can’t terminate it “one step short” with the universe: just as God supposedly “just is”, so the universe actually “just is”. Yet the same could be said of the past, on Russell’s five minute hypothesis. Instead of supposing that there are (or were) “past events” that took place before five minutes before your reading this entry in order to explain current events, why not invoke Occam’s Razor and eliminate them, since the subsequent events could exist without supposing any previous ones? Nevertheless, supposing the universe sprang into existence five minutes ago is deeply counterintuitive. And in rejecting the remote past, our dramatic gain in parsimony is accompanied by a tremendous loss in explanatory power, for now the is no account to be had of why the present is the way it is, or why it even exists at all.
In addition in induction and deduction, it is often said that there is a third kind or reasoning called abduction, which is also known as “inference to the best explanation.” On my own understanding, the basic principle behind abduction goes something like this:
(1) Given some target phenomenon and multiple theories vying to account for it, it is most reasonable to posit that the theory which best explains the phenomenon in question is the correct one.
I believe this principle can be extended to say that:
(1') Where it is possible to posit an explanation for something, and also possible no to posit an explanation, then, if there is no evidence against the hypothesis that there is an explanation, it is more reasonable to posit one than not.
(1') would (presumably) override Occam’s Razor and justify us in positing events that took place previous to those that took place five minutes ago. But by similar reasoning, wouldn’t this justify us in positing a first cause? For if it is indeed more reasonable to posit an explanation than not where it is possible to do so, shouldn’t we posit an explanaion in the case of the universe? Since there seems to be no evidience against the hypothesis that the universe has an explanation, the principle would licence the postulation of some explanation.
Now, it may be objected that since the universe includes everything it is incapable of being explained by anything outside it. This well and goods as far as it goes, however, it is a contentious reading of the term “universe”. If we define the term “universe” to include everything that exists, it is indeed incapable of explanation by anything “outside” it, but then God (or some ‘first cause’) may very well be included in the totality of everything that exists. But if by “universe” we simply mean the physical universe, it isn’t at all obvious that it has no outside explanation or that it is incapable of having one.
Cosmological arguments for the existence of God usually being with the existence of everyday objects and events and argue that these stand in need of explanation. The causes that are invoked to explain them, however, stand in need of explanation just as much as the things we started with. Eventually this regress is supposed to terminate in a first cause, which many argue is identical to God on some suitable understanding of the word “God”. If (1') is correct, then at each step in the regress it seems possible, even if not necessary, to posit an explanation, and thus (1') will drive us to posit some explanation for what we are at that stage considering. And if we agree with Leibniz that even an infinite regress of causes stands in need of an explanation as a whole, we can continue applying (1') indefinitely, until we are driven to posit a first cause, which ultimately explains everything outside itself. After all, if it is possible to posit something that explains (almost) everything, (1') would seem to counsel that it is more reasonable to posit it than not.
So what, if anything, is wrong with the above line of reasoning? Might it be that we are equally unjustified in positing a first cause and the existence of the remote past? Is (1') too strong? If it is, then what else could override Occam’s Razor and justify us in positing remotely past events? If nothing else, the version of the cosmological argument given above has the benefit of not invoking the “principle of sufficient reason” or any hypothesis of the necessity of universal causation. The argument has instead been couched in terms of rational belief, and is perfectly compatible with the metaphysical possibility of causeless events. So long as we are not overly hasty in identifying the "first cause" with a much more robust notion of "God", there seems to me to be nothing overly contentious in the argument. But whether that is so is for the reader to decide.
 I’m indebted for the above paragraph to Scott Ryan, who brings out this point very nicely in chapter 11 of his book “Objectivism and the Corruption of rationality”.