The very definition of the universe is that it is everything around us. Obviously.
The space that the universe takes up has to be infinite, because if there was a barrier at the edge of the universe, no matter what it is (simply a wall, or what? more empty blackness), that too would have to be included as part of the universe.
The reasoning that the universe could wrap back around on itself, would also require a defined area that the universe was taking up.
You give the example of the round earth or cue ball having no "end", on its surface, but the universe is far from the linear surface of a sphere.
This topic is at the very limits of human comprehension. Humans can only learn about things on a basis of comparison. A concept like infinite is far too great for the human brain to conjure up. Where else do we see infinite, only in math, and math is known as the interpretation of the scientific. Infinite exists in math, we are still unable to explore all of it, because it is infinite.
Time and space are, in a way, like the X and Y axis of the universe. They are interdependant on eachother and you can't really escape either. They also can both be warped together, theoretically, by going the speed of light. Now, if we think about time, it HAS to be infinite. The very definition of time, is that it will go on forever. You can imagine, that if the world wasn't here, time would still relentlessly "tick" on as it has for.....ever.
I believe that both time and space are infinite. It is a just a fundamental law of all that is. For the universe to have not existed at one point would make you realise that something affected it to come into existence. Now, don't think of God or something doing this, because we are left with the same problem.
Suppose that the universe was infinite in both time and space, we are basically not capable of understanding something like this. But I think it could be a law, that the universe, has and always will exist, as an expanse of space that has no end.
Just like the law that all matter has gravity. Why is this law imposed on all matter? Who knows, it is just programmed into the properties of the universe.
If you are patient I will give you all some idea of the vastness of just the visible universe.
I really think that most people don't realize how big the universe is.
If you have ever done a scale model, I will tell you how it would work, listen carefully and you will be blown away.
To get an idea for the earth in relation to the sun, you could hold a sphere, that has the diameter of a CD. That is the sun, now the earth on this same scale would be exactly half the size of the hole in a headphone jack for your walkman. (Not the big headphone jack on your stereo.) And, on this same scale they would be exaclty 53 ft apart from eachother.
Also, on this same scale Pluto (the furthest planet from the sun in our solar system) is the size of the period at the end of this sentence. On our scale model it would be 600 meters away. 0.6 of a kilometer or 1/3 of a mile away from our CD sized sun.
Now, to give us a perspective on the next closest star, Alpha Centauri, we have to shrink our scale even more. The sun is now 1 grain of salt, and the earth is 1 single grain of talcum powder (which is VERY small). The grain of talcum powder (earth) is 4.3 inches from the grain of salt (sun).
The next closest star, Alpha Centauri would be the size of a SLIGHTLY smaller grain of salt, and that would be 17 miles or 33 kilometers away. ABout a 20 minute drive at highway speeds, to get to this other grain of salt.
Now, we are 1 star in the Milky Way Galaxy. In the milky way galaxy there are over 100 billion solar systems like our own. All about as far apart as our sun is from Alpha Centauri. If we made a scale of the Milky Way galaxy using the grain of salt size stars the diameter of the Milky Way would 425,000 miles (684,000 kms) full of over 100 billion grains of salt. All these grains of salt are between 15 and 20 miles apart.
425,000 miles is FAR more miles than the average car gets in its lifetime. If you started at one side of our scale Galaxy, with a car that was travelling 60 mph or 100 km/h (highway speed) and you didn't stop or even slow down for a second, it would take 295 days to drive across this scale galaxy. Or just under 10 months.
Now, that you have our galaxy roughly imagined in your head, although it is VERY difficult for us to picture a swirling mass that is 425,000 miles large, even on our 1/10 billion scale.
The Milky Way is part of a Super cluster. In a super cluster there are about 200 million Galaxies.
In just the visible universe, which is only as far as we can see, there are over 50 million superclusters.
To get another perspective, just imagine this:
The number of stars in the visible universe is more than the number of grains of sand on EVERY beach in the world.
At this point your brain is probably mush. Everytime I think about this, I am blown away.