Simple conservation laws and universal induction. The alternative is self-contradiction.
Given that something exists or is on a certain trajectory, the claim or hypothesis that the object ceases to exist or changes its trajectory or other properties without a cause is the most absurd possible posit.
Turning the question around, why would we assume that infinite regress is somehow fallacious or logically weaker than unobserved speculations such as acausality or existential discontinuity?
Infinity in reality is not at all difficult to comprehend. Every moment up until now has elapsed. Add one more, and the present has arrived. Keep on doing that, and you have the infinite. Whatever the present situation, infinity always comes down to the condition of there being at least one more. Infinity is not a number, it is the principle that whatever has been accomplished so far is in the process of augmentation, regardless of when we measure it.
The arrival of another moment is an embodiment of the law or principle of conservation, therefore infinite or unbroken continuity is the expected result in questions of existence and consequence, while there is nothing more absurd than an existential terminus. It would violate all rationality and causality to "find" or allege the existence of breakages of eternal law.
In terms of infinite regress of chains of causality, one does not have to prove closure by brute force enumeration. All one has to do is to have a testimony that a law or principle is inviolate to prove by induction that a terminating case cannot exist. The conservation of matter is a very germane law. It holds true, therefore matter "poofing" into or out of existence would only prove the insanity of the one speculating such a contradiction.
Infinite regress is therefore fully resolved by simple proofs of induction.
N+1 will always be greater than N. One does not have to sample every hypothetical value of N to prove this.
Matter is conserved, therefore it never had a beginning.
The first verse of the Bible agrees with this statement. The Hebrew word bara' denotes "to shape, form, or fashion", as in cutting wood, not "to cause to poof into existence from nothing". The latter is a contrived and nonsensical meaning.
Contemporary imagination, schooled by Hollywood, is not a good guide, nor, apparently, are the creeds of the Dark Ages. The truth was spoken when this Earth was formed by its Creator.
Can anything be outside of time?
Logically, it can be easy to contemplate the existence of eternity as "external" to a temporal organization. That is to say, that things have their time or their temporal existence (as an organized body), and their own measurement of time.
For example, one can measure time on a watch after it has been made and wound up.
In exactly the same way, one can measure time in terms of the revolutions of a planet after it has been formed and set into orbit around a larger body.
When the watch has stopped ticking or the planet has spiraled to its doom, does it make sense any longer to speak of time as measured by that instrument? I can hardly think that it would be; that would be a relativistic and over-specified, moreover inadequate definition. When the instrument ceases functioning then the instrument of measure would contradict its former self. One will need to commission new instruments to keep track of time when the old instruments have expired.
In this sense there is "a beginning" and "an ending" as measured from each organized body that has a finite span of service, but to me the idea that things were frozen and then magically thawed or that they will freeze in the future so that nothing more can happen, are both absurd propositions because they violate eternal law.
I am not a believer in a non-progressional concept of eternity. By non-progressional I mean "things have stopped happening".
The useful lessons we learn about time and the importance of proper prioritization here will be of great value in the future, and are conserved, being eternal in nature.