I want to contribute to this post, so here goes. In the beginning, the actual point, though smaller than infinitesimal, actually if we go to the realm of Plank in size, mass, and time, we find a point beyond which we cannot go mathematically. Thus if the Math does not work, no one can observe or guess at what is actually there or happening. Plank size is so small it is beyond comprehension. So the Math tells us that the Big Bang started here, at the level of Plank size. We say this because the Math tells us it does. So what-ever happens happens, and the Universe starts. Kind of like an explosion, not really as explosions take place on the scale we can see what happens and understand what is going on. Not an explosion in that sense, the explosion did not take place at a time as there was no time to be observed at this point, neither was their space as it had not been created as of yet. The "explosion" happened and space-time was created as this process started to exist and create it. There is a law of physics that states that nothing can traverse within space-time faster than the speed of light. This is true, however Space-time itself can move at any speed it wants. This is what Einstein's equations led to. So Kluth's "inflation" tells us that space-time can expand at any rate it wants as it is space that is moving within itself as it comes to exist. This leads us to the fact that the Universe is now ninety two billion light years across, we can only know of 13.4 billion light years into the Universe. This gets really confusing. We know the Universe is 13.6 billion light-years across because we can actually see the light from this distance. This means that that light was there 13.4 billion years ago. Which means the Universe is larger than 13.4 billion light years. Thus the figure of 92 bly across. Space-time fills all the Universe. What is outside the Universe? This is not known as we will never know as the edge of the Universe is beyond our ability to see. If we could see the edge of the Universe we would see it as it was long ago what the light was at that place in the Universe. Someone has mentioned that the Big Bang is a crime against the People. This is bullshit as it is a conclusion that was developed by looking at data. Now there can be another take on this data and come up with a different conclusion, but whatever one comes up with the data has to show how they logically flow from each other. I can postulate a theory, I can say data exists that proves this to be true. but unless others who have the same or higher educational and ability to deal with the data agree, my theory is wrong. If others agree than I am correct. At any time some other data can arrive that shows one or the other of us to be correct or incorrect. Science goes to the concept that has been proven to be the best by all, every theory can have its detractors. Science gives us much, it is correct and useful. We have much that has been developed from it, many can give it pause as it does not have everything figured out. When Scientists say that there isa problem with Quantum Mechanics they do not mean that QM could be disproven or wrong. Our understanding may have problems but GPS works, the computer I am writing this on works, electricity works, as does much of the research for cures most of us suffer from. Their concern does not mean the world is going to quit working. Thoughts? Questions?

No one knows, and know one will ever know.
Don't get me wrong, I like science and, Einstein probably had the best answer because, it is an answer.
I believe there is always a reaction to am action, and it is because of that things continue, things replicate, things evolve, things begin...it is a reaction to an action as particles dance among each other bumping into each other which sparks something else. That will just keep going...until it doesn't.
**Below...not a source just an interesting read.

Beginning :: we don't know.
End: :: we ain't there yet.

Any thought about David Talbot, Walt Thornhill & Don Scott’s Electric Universe Theory? Their research seems to be standing up

We have no evidence of a beginning to the Universe approx 13.7 billion years ago. We have Georges LeMaitre’s fraudulent attempt to support the Genesis story.

Edwin Hubble summarized his hypotheses in the 1937 Royal Astronomical Society Monthly Notices:
“If the red shifts are a Doppler shift . . . the observations as they stand lead to the anomaly of a closed universe, curiously small and dense, and, it may be added, suspiciously young.
“On the other hand, if red shifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely in both space and time.“

From Hubble’s first “If....” hypothesis, LeMaitre wrote equations with time the independent variable. He ran time backwards, giving the Vatican support for Genesis and America’s fundamentalist xians a response to Darwin. Many astronomers disagreed but wanted to do astronomy. They did not want a political fight with America’s xians.

@Shynight I have much knowledge of astronomy and physics.
You asked is time and space eternal in the universe?
Astronomer Edwin Hubble said the universe is “extended indefinitely in space and time.“
The Big Bang is a big fraud on the taxpayers.

“The Myth of the Beginning of Time”

[scientificamerican.com]

Such questions are framed from the perspective of our space/time/matter model of reality, which is an illusion. According to quantum gravity theory, time does not exist, and space consists of a finite number of granules.

If that theory turns out to be correct our most basic concepts of creation, causality, location, motion, and even existence itself are not meaningful from a cosmic perspective.

Read Reality is not What it Seems by Carlo Rovelli.

Your first question involves a circular argument. The answer to your second question depends on debate currently happening among cosmologists, as time might only have become observable at the Big Bang, and the fate of the universe is as yet unknown.

That is a complex question. But I will give the shortest version of an answer that I can.
As far as Eternal. We have no real empirical evidence to know one way or another.
In a mathematical perspective, there are leaps and bounds of possibilities. Alternate universes, Multiple universes, and many more.

As far as we know. the relationship between, and including Space/ time. is and is not a constant, Sorry for the seemingly contradiction, but it is however true to the best we know.
on a cosmic scale we have an ongoing theory. But to be honest, even that has some pitfalls, including Alan Guth's addition of 'inflation' theory. which tries to explain how our universe just happen to grow in an exponential rate. But there is no real Science to back that up. It is just accepted.

Einstein's Relativity, and Special Relativity for the most part do describe how Space, and time are curved. in essence, the more something weighs, the more of a dent it puts in the Space/ time grid. With that in mind. Time is relative to those curves. The greater the dent, the greater that time is affected.
You wouldn't notice it from say our earths dent, although, it does have some effect.
But when you get into the realm of super massive, or super dense objects. Like for instance a black hole, or neutron stars. Time dialates some times exponentially.

Meh, sorry I can go on a tangent at times.

Given all of that. One thing, no matter the speculation, is that we really don't know much about how everything started. Or, if it will ever end. Granted, there is a bit of circular reasoning there. But that is the state we find ourselves in trying to figure out all of those questions.

Shit. Did I just give a longwinded yap about nothing. Meh.
In truth, we just don't know.

My best advice is to seek these answers on you tube where actual scientists, physicists, astronomers and cosmologists can explain much better than I. But I've had the same questions for as long as I can remember and still have a hard time wrapping my head around it all.

There could only be infinity of space in every direction. Science likes to create and would say that the word "bang" created the universe and started pushing back anti-space creating the scientific space-time bubble.

However, as I see it, space is not a thing. That is, space is not a substance.

Space has always been and always will be.

Yes, space and time is eternal, people have starting and ending points.

Nothing is sternal. After enough time has passed, the universe in its entirety will cease to exist.

There is no space, there is no time -- only spacetime :

[scientificamerican.com]

[einstein.stanford.edu]

[space.com]

Would you prefer us to guess and pretend we know? We might never know.. which makes things frustrating when dealing with people who assert they know and can't demonstrate it!

We don't know yet. Maybe we never will. Any other answer would be speculation.

Excellet question. So excellent that know one has an answer.

I would say that time and space are eternally infinite.