SuttaCentral
Indeed! A well spotted possibility!
But such an extraordinarily depressing one. If the hell realms are infinite, then any finite number of higher beings is essentially a zero blip in an endless sea of hell 
Perhaps this is why the Buddha warned that
Well… at least that theory does motivate you to enter the stream and get out of here!
I was aware that this is a point of Mahayana speculation, but I wasn’t aware that they were extrapolating from the same EBT quote I mentioned above (cool!) nor did I know about that particular text, so thank you for sharing! 
Thanks for that quote! It actually lends evidence to the infinity of beings in my opinion, as the percentage of beings saved would be “0%” But since that’s a rather depressing and confusing answer, I can see why the Buddha would rather choose to remain silent. 
Back on the subject of EBTs and how non-EBTs get incorporated into the corpus of Buddhavacana, you’ll notice that the Sanskrit recension is called a nirdeśaparivarta, a treatise, and the Chinese recension is entitled “The Buddha Speaks the Lack of Increase, Lack of Decrease Scripture,” how things change. That is part of the process of how this text goes from being a treatise on cosmology to a tathāgatagarbha sūtra.
So, if I’m to summarize what we’ve found so far:
Does this sound right to everyone?
I physics there’s the concept of event horizon.
In practice it encapsulates the beings in a sphere beyond which, due to expansion of time-space, light ( the fastest thing) will never reach.
This effectively limits one’s observable universe at any given point in time.
This horizon serve as an edge for causality.
Given that we are dependent originated streams aggregates of suffering, born of causation, I argue that event horizon serves as a limit to what we can affect with our choices and actions (including observing and knowing).
Hence, while it may be the case that an infinite amount of timespace stretches beyond or event horizon, for the sake of shared samsaric experience we may be stuck with those within the same “radius” of timespace.
The topics below may be interesting to understand the geometry of causality.
It seems to me this question falls under the imponderable category of questions that bring madness to anyone who conjectures about them per AN 4.77. Specifically the fourth category in that sutta.
How so?
As I understand them, the sutta statements that saṃsāra is without conceivable beginning, and that there is no first point to avijjā, mean that all beings that exist have always been transmigrating. We didn’t start doing so at some particular point in the past. I don’t see how any conclusion could be drawn from this as to whether the transmigrating beings are limited or unlimited in number. Both possibilities would be equally compatible with the claimed beginninglessness. The only thing that is ruled out is the possibility of a completely new khandha-continuum coming into existence.
Agreed.
Perhaps to hedge our bets we should just focus on infinite metta, compassion, rejoicing and equanimous inclusivity for all, regardless of number.
Monotheistic religions say everything in this world has a beginning. The god created it at some point in the time. When they say so, they end up with a lot of questions. Why that particular moment, why not before? Who created the god? He lived all along?
When someone come up with a beginning, always draw into another problem.
Buddhism explains a existance without a beginning and that solves the problem. Then some ask what if all of the beings attain nibbāna? There wont be any in the universe. This is a stuation similar to above problem in monotheistic religions. Thats why both possibilities would not be equally compatible with the claimed.
Some argue there may be a way that generates beings however, that should not be the case since the blessed one said there is no beginning to the samsāra.
The questions that you think ought to bother a theist were actually anticipated and answered 1600 years ago by St Augustine.
In a nutshell, Augustine held that along with the heavens and the earth, time itself was created by God. And so Augustine would simply retort that your questions are based on a mistaken assumption, namely, that God “created the world at some point in time.”
“But if there was no time before heaven and earth, how, then, can it be asked, “What wast thou doing then?” For there was no “then” when there was no time.”
[…]
“There was no time, therefore, when thou hadst not made anything, because thou hadst made time itself. And there are no times that are coeternal with thee, because thou dost abide forever; but if times should abide, they would not be times.”
(Confessions XI)
Augustine, Confessions Book XI
Eric Rosenfield, An Analysis of the Concept of Time in the Confessions
In what sense would the absence of beings in the universe be a problem?
My phrasing was a bit wrong. Here, that is not the case anyway.
End up with a similar problem.
As the samsāra has no known beginning, why we are still here. We could have been long gone by now if the number of beings has a limit; thats why.
Therefore, this creats somewhat a paradox.
That would only be the case if saṃsāra conformed to the Ājīvakas’ “ball of string” model, wherein the end of suffering comes about through the mere elapse of sufficient time:
Makkhali Gosāla:
“Though one might think: “By this moral discipline or observance or austerity or holy life I will ripen unripened kamma and eliminate ripened kamma whenever it comes up”—that cannot be. For pleasure and pain are measured out. Saṃsāra’s limits are fixed, and they can neither be shortened nor extended. There is no advancing forward and no falling back. Just as, when a ball of string is thrown, it rolls along unwinding until it comes to its end, in the same way, the foolish and the wise roam and wander (for the fixed length of time), after which they make an end to suffering.”
DN. 2
This is not what I was telling.
Eventhough beings should have to practice the path and achieve Nibbāna, they got three different bodhis; Buddhahood, pacchekabuddhahood, Arahanthood.
There should have been unlimited number of buddhasasanas in past (as the samsāra has no begining). Logically, each being in the world should met their chance to practice dhamma. Why would someone drawn into Makkhali Gosāla’s ditti at all to put up the paradox.
Logically?
At least in imagination we might conceive of a being who throughout his wandering in saṃsāra simply never acquired merit of the kind that would be a cause for his encountering a buddhasāsanā. Is there really any principle of Dhamma that would logically rule out the possibility of such a being? I don’t myself see one.
Perhaps in the Ājīvaka system saṃsāra wasn’t considered to be beginningless. At least that’s the only way I can see that followers of Makkhali might escape the charge that their teacher’s doctrine is falsified by the fact that dukkha isn’t yet universally extinguished.
Making a theory is always has some cognitive biases. You have yours and I have mine.
Cattārimāni, bhikkhave, acinteyyāni, na cintetabbāni; yāni cintento ummādassa vighātassa bhāgī assa. Katamāni cattāri? Buddhānaṃ, bhikkhave, buddhavisayo acinteyyo, na cintetabbo; yaṃ cintento ummādassa vighātassa bhāgī assa. Jhāyissa, bhikkhave, jhānavisayo acinteyyo, na cintetabbo; yaṃ cintento ummādassa vighātassa bhāgī assa. Kammavipāko, bhikkhave, acinteyyo, na cintetabbo; yaṃ cintento ummādassa vighātassa bhāgī assa. Lokacintā, bhikkhave, acinteyyā, na cintetabbā; yaṃ cintento ummādassa vighātassa bhāgī assa. Imāni kho, bhikkhave, cattāri acinteyyāni, na cintetabbāni; yāni cintento ummādassa vighātassa bhāgī assā
In AN 7.62 we read:
I recall undergoing for a long time the likable, desirable, and agreeable results of good deeds performed over a long time. I developed a mind of love for seven years. As a result, for seven eons of the cosmos contracting and expanding I didn’t return to this world again. As the cosmos contracted I went to the realm of streaming radiance. As it expanded I was reborn in an empty mansion of Brahmā.
2There I was Brahmā, the Great Brahmā, the undefeated, the champion, the universal seer, the wielder of power. I was Sakka, lord of gods, thirty-six times. Many hundreds of times I was a king, a wheel-turning monarch, a just and principled king. My dominion extended to all four sides, I achieved stability in the country, and I possessed the seven treasures. These were my seven treasures: the wheel, the elephant, the horse, the jewel, the woman, the treasurer, and the counselor as the seventh treasure. I had over a thousand sons who were valiant and heroic, crushing the armies of my enemies. After conquering this land girt by sea, I reigned by principle, without rod or sword.
That’s a lot of beings and a lot of time.
This sutta is baffling. What could it mean?
I don’t think the meaning is really recoverable now. Though luckily the part Amatabhani refers to is a summary of Makkahali Gosāla’s dhamma, not the Buddha’s.
Transmigration has no (known) beginning
Therefore, there is a possibility of infinite number of buddhas.
If there are infinite number of beings, no matter how many buddhasasanas appear time to time all of them would not achieve Nibbāna.
If the number of beings are finite in a transmigration which has no beginning, they would eventually reduce in number. So they should have met Buddhas in the past and achieved Nibbāna. Why are we still here.
Only way this could happen is having infinite number of beings in the universe.
This is no Makkahali Gosāla’s dhamma but just an argument.
I do not say that beings would eventually achieve Nibbāna doing nothing. They should practice eight fold path to achieve Nibbāna.
However, finite number of beings in a beginningless transmigration is not possible. That is what I was trying to say.