In Buddha's Middle Discourses (Majjhima Nikaya), Buddha is asked by one of his followers about his view on the eternality and infinitude of the world:

Majjhima Nikaya - Aggivacchagotta Sutta 3-6

3 "How is it, Master Gotama, does Master Gotama hold the view: 'The world is eternal: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The world is eternal: only this is true, anything else is wrong.'"
4 "How then, does Master Gotama hold the view: 'The world is not eternal: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The world is not eternal: only this is true, anything else is wrong.'"
5 "How is it, Master Gotama, does Master Gotama hold the view: 'The world is finite: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The world is finite: only this is true, anything else is wrong.'"
6 "How then, does Master Gotama hold the view: 'The world is infinite: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The world is infinite: only this is true, anything else is wrong.'"

Buddha's response above is essentially to refuse to answer, or take a position on either question. He denies that he holds the view that the world is eternal, or that it is not eternal. He denies that he holds the view that the world is infinite, or that it is finite. This means that he has no view on these questions - he is agnostic.

Buddha's follower continues with his questions, proceeding to ask about the relationship of the body to the soul, and whether an enlightened person (Tathagata) continues to exist after death:

Majjhima Nikaya - Aggivacchagotta Sutta 7-12

7 "How is it, Master Gotama, does Master Gotama hold the view: 'The soul and the body are the same: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The soul and the body are the same: only this is true, anything else is wrong.'"
8 "How then, does Master Gotama hold the view: 'The soul is one thing and the body another: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'The soul is one thing and the body another: only this is true, anything else is wrong.'"
9 "How is it, Master Gotama, does Master Gotama hold the view: 'After death a Tathagata exists: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'After death a Tathagata exists: only this is true, anything else is wrong.'"
10 "How then, does Master Gotama hold the view: 'After death a Tathagata does not exist: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'After death a Tathagata does not exist: only this is true, anything else is wrong.'"
11 "How is it, Master Gotama, does Master Gotama hold the view: 'After death a Tathagata both exists and does not exist: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'After death a Tathagata both exists and does not exist: only this is true, anything else is wrong.'"
12 "How then, does Master Gotama hold the view: 'After death a Tathagata neither exists nor does not exist: only this is true, anything else is wrong'?" "Vaccha, I do not hold the view: 'After death a Tathagata neither exists nor does not exist: only this is true, anything else is wrong.'"

Notice that just as with the eternality and infinitude of the universe, these are extremely fundamental questions about reality. And, similarly, Buddha remains agnostic, refusing to take any position.

Likewise, in the Culamalunkya Sutta of the Middle Discourses, Buddha is asked the same set of questions by a different person, responding:

Majjhima Nikaya - Culamalunkya Sutta 7-10

7 "Therefore, Malunkyaputta, remember what I have left undeclared as undeclared, and remember what I have declared as declared. And what have I left undeclared? 'The world is eternal' - I have left undeclared. 'The world is not eternal' - I have left undeclared. 'The world is finite' - I have left undeclared. 'The world is infinite' - I have left undeclared. 'The soul is the same as the body' - I have left undeclared. 'The soul is one thing and the body another' - I have left undeclared. 'After death a Tathagata exists' - I have left undeclared. 'After death a Tathagata does not exist' - I have left undeclared. 'After death a Tathagata both exists and does not exist' - I have left undeclared. 'After death a Tathagata neither exists nor does not exist' - I have left undeclared.
8 "Why have I left that undeclared? Because it is unbeneficial, it does not belong to the fundamentals of the holy life, it does not lead to disenchantment, to dispassion, to cessation, to peace, to direct knowledge, to enlightenment, to Nibbana. That is why I have left it undeclared."
9 "And what have I declared? 'This is suffering' - I have declared. 'This is the origin of suffering' - I have declared. 'This is the cessation of suffering' - I have declared. 'This is the way leading to the cessation of suffering' - have declared.
10 "Why have I declared that? Because it is beneficial, it belongs to the fundamentals of the holy life, it leads to disenchantment, to dispassion, to cessation, to peace, to direct knowledge, to enlightenment, to Nibbana. That is why I have declared it.

Above, Buddha said that he remained agnostic on many matters pertaining to the fundamental nature of reality because "it is unbeneficial, it does not belong to the fundamentals of the holy life, it does not lead to disenchantment, to dispassion, to cessation, to peace, to direct knowledge, to enlightenment, to Nibbana". Instead, according to himself, he only taught on the origin of suffering, and the means of attaining the cessation of suffering.

Buddhism, therefore, can never be anything more than a philosophically deficient religion. There can be no answer, or even speculation, on such things as how the universe exists, the nature of a person's soul, or even existence after death - all fundamental, vital questions, which define how a person views reality. The founder of the religion has declared such topics "unbeneficial", and elsewhere "beset by suffering, by vexation, by despair" (Aggivacchagotta Sutta 14).

Consider some of the implications of Buddha's agnostic approach to these fundamental questions of reality:

• If the universe is not eternal, then it must have been created at some point, by an agent intelligent enough to design it, and powerful enough to create it. This position, therefore, would directly imply the existence of a personal God, who is eternal. This, however, would have massive implications for a person's view of Buddha, and the religion that he created. This God would be the designer of Karma, and rebirth. He would be the one who made all the rules for how it works. So, if Buddha were to venture to tell humanity how to escape Samsara (rebirth), he would logically need to have been commissioned by this God. Why else would anyone care what Buddha has to say? Without a divine commission, or even claim of divine revelation, he has no basis for asserting that following his method will stop someone from being reborn. His authority depends on God existing, and him having been sent by that God, with the correct method to stop the cycle. Of course, the same can be said of Buddha's teaching, borrowed from Hinduism, that rebirth is taking place in the first place, and that karma is operative on that process. Why would anyone believe Buddha's assertions that these things happen, if he has not received revelation from God that they take place?
  
  Suppose, on the other hand, that the universe is eternal. Then, there are a few options regarding God and His relation to it. He could be co-eternal with it. He Himself could be the universe. It could constitute a part of Himself. Each of these things would have massive implications for Buddhism, and one's view of Buddha, for the aforementioned reason - if God exists, one should get their information on the nature of reality either from Him, or from one that He directly communicated with, or gave knowledge to. Otherwise, there is no reason to believe someone's speculations as to the nature of reality, such as the existence of rebirth.
  
  In any case, Buddha's system definitely seems to imply that there must be a transcendent, intelligent agent, if for no other reason than someone needed to design the Karmic system of rebirth on which Buddha's religion is based. Otherwise, who made the rules? Who decided that sentient beings would exist, and need to learn to cease bad desires, or otherwise be reborn? Who is managing that system? And, otherwise, why should anyone believe Buddha's speculations on the nature of reality?
  
  Yet, consider how unfinished and deficient the necessity of God renders Buddha's religion. His religion requires a God, and the existence, nature, will, and identity of that God would have massive implications for every aspect of Buddhism, and yet, Buddha failed to define the universe's relationship to God, by failing to teach that He created it, or is co-eternal with it, or something else.


• If the soul is the same as the body, then when the body is destroyed, a person would cease to exist, and the entire basis of Buddha's religion - the cycle of Samsara - would be refuted. Buddha's religion requires a non-material component to a person, which remains identified with that person after death, and across potentially innumerable bodies. So, Buddha's religion seems to absolutely depend on a person's body not being the same as their soul. Therefore, his agnosticism on the subject does not really make sense.


• If one who reaches enlightenment does not continue to exist after death, then whatever created sentient beings, and designed Samsara, wanted those beings to (1) exist, (2) learn that existence is to suffer, (3) follow Buddha's method to cease desire, then (4) cease to exist, which is absurd, and pointless. In such a situation, the one responsible for the existence of sentient beings, and Samsara, will have created a cosmic torture chamber, for no reason.
  
  On the other hand, if an enlightened person continues to exist after death in some form, then this would have massive implications on Buddhism's doctrine of the self, its relation to God or the ultimate reality, the purpose of sentient beings, and much more.
  
  In any case, this is considering the final result of following Buddha's religion. By remaining agnostic on this issue, he literally refused to teach on what happens to one if they listen to him, and follow his method.

Conclusion

Buddha did not have answers to many of life's most important questions, because he created an errant, deficient philosophy, which was unable to accommodate many of life's most important questions.

Consequently, there are no answers in Buddhism. A person's origins, nature, and fate are all purposefully forbidden to be speculated on, lest they distract from the method that the religion's founder insists, based on his own authority, will solve a person's problem of Samsara (rebirth), which he insists takes place, also based on nothing more than his own authority.

The contrast of this philosophy with richness of the true God, who has infinite love for mankind, and made them for the purpose of having them share in that love, cannot be more extreme. This is why, when confronted with the true God, and His love for them, so many Buddhists have left their religion, valuing coherence and truth more than the vain philosophy of their forefathers:

Jeremiah 16:19

19 O LORD, my strength, and my fortress, and my refuge in the day of affliction, the Gentiles shall come unto thee from the ends of the earth, and shall say, Surely our fathers have inherited lies, vanity, and things wherein there is no profit.