Physicists have a lot of very good evidence that the universe inflated from a singularity, a single point, approximately 13.8 billion years ago. Some of the evidence comes indirectly from mathematical models, but physicists can also detect and investigate the echo left from this time because that echo remains today. The entire universe is bathed in a sea of microwaves, called the cosmic microwave background (CMB). The CMB is direct evidence for the Big Bang theory, as it is called. If you have an old TV set you can see CMB photons contributing to the static on the screen. This echo is still here because it has nowhere else to go.
The unimaginable energy (here, think about all the current matter and energy in the entire universe squeezed into a microscopic space) of the Big Bang unleashed a fury of extremely energetic photons called gamma rays. They shot around in every direction, crashing into other particles. Some of those photons are striking Earth today billions of years later, but as microwaves rather than gamma rays (fortunately). About 300 photons are flying through very square centimeter of space right now. There are so many of them, only a tiny fraction of them have stuck other particles and transferred their energy into other forms. Where are they coming from?
To get our answer we need to take a look at the expansion of the universe. No one knows why the universe expanded from a single point or what existed, if anything, before that. What physicists do know is that the Big Bang was the origin of both space and time, as we understand it. Space and time are described as dimensions in a four-dimensional theory called general relativity. Physicists can theoretically trace events back to about 1/32nd of a second after the universe popped, or banged, into existence. Before that time, current theories about how space-time operates break down into nonsense, so it is impossible to peak into the very first moments of our universe.
Shortly after the Big Bang (a tiny fraction of a second), the universe, according to most well established theories, went through a brief period where its expansion rate increased to faster than light speed. Physicists can prove that galaxies farthest away from us are also traveling away faster than light speed because we are now once again in an era of accelerating expansion. These two periods of accelerating expansion owe themselves to different mechanisms.
All of this faster than light business does not violate the special relativity rule that says that nothing, even light, can travel faster than light speed, because space-time ITSELF is the thing doing the moving, or expanding in this case.
How can we see the CMB when it is the oldest stuff in the universe? Shouldn't all those photons be invisible because they are moving away from us faster than they could travel toward us? The CMB permeates the entire universe. That includes the part of the universe that is not moving away from us faster than light speed. This is the CMB that is detectable. Everything is traveling away from everything else in the universe but the expansion is cumulative. You can't even detect it on the scale of our own galaxy but as you get further and further away over great distances, that miniscule expansion rate accumulates so that as you observe regions very far away, you are seeing photons coming from very old stars and their motion is approaching light speed. There is evidence of a much larger invisible universe outside the boundaries of the visible universe. Photons in this outer region will never reach us so it is invisible to us. When you look at the oldest stars you are seeing stars that are long burnt out. You are seeing the light that shone from huge white-hot stars that were born when the universe was just hundreds of millions of years old. In other words you can see ghost of stars that once were. There may currently be new stars in that region that are generations younger but their light hasn't reached you yet.
Expansion of the universe had a significant effect on CMB. Each photon travelling randomly through space travelled while that space expanded. As space expanded, the wavelength of each photon was increasingly stretched across it. What started as very short wavelength gamma photons are now long wavelength microwaves. We can no longer see them because they are now in the invisible part of the spectrum. If you could put on glasses that let you see in the microwave spectrum, you would see the universe glowing all around you. You might be wondering: does this mean that those photons lost their energy to space somehow? No, although this "tired light" hypothesis had some traction decades ago, apart from colliding with other particles and transferring their energy, photons retain as much energy as when they were created. There is no "friction" in the vacuum of space.
An important point to keep in mind is that there is nothing outside the universe, at least according to most theories. A common analogy used to think about the expanding universe is an expanding balloon, but there are some key differences. While a balloon expands into the space around it, there is no space for the universe to expand into, not even a vacuum. The surface of the balloon is a two-dimensional surface expanding outward, whereas the universe is expanding spatially in three dimensions. You can get a simplified idea of what the expansion looks like if you draw a few dots on a balloon with a marker and then blow it up. The dots grow further and further apart from each other as the balloon expands. In reality, however, the dots, which are galaxies of stars, are embedded in the substance of the balloon. A better analogy might be raisins moving apart from one another in a rising loaf of bread. There is an additional quality of space-time that the balloon doesn't illustrate. All the matter dotted throughout the universe affects space-time. It stretches space-time's four-dimensional fabric. Space-time stretches as the universe expands, taking everything in space along for the ride, but matter itself also stretches space locally. Like a bowling ball on a trampoline, a massive object such as a galaxy makes a depression in space-time, except the depression is in four dimensions rather than in three.
Space-time is also a relative fabric. The theory of special relativity says that how a section of space-time looks and behaves depends on how fast you are traveling relative to it. Think of an object like a spaceship travelling close to light speed through space relative to you. In other words it could be flying through space past you as you float in a space station. Its spatial length would appear to be squished. It would look like a short squat ship. It would appear as thin as sheet of paper if it were going almost exactly light speed. People on the space ship wouldn't notice anything weird. The ship's time frame would also stretch. Those people could travel to some planet light years away, settle down and colonize, and still be decades younger than you when they returned for a visit. The movie, Interstellar, illustrates this unsettling effect very well. Exactly at light speed, relative time stops altogether. If you could hitch a ride on the back of a photon, your children would live their lives, the entire history of mankind would play out, in fact the universe would unfold to its end around you and you would not have time to even blink. It would all play out instantly to you. Time also plays this tricky maneuver at the event horizon of a black hole. In this case, time slows down relative to the space around it because space-time around a massive black hole is stretched infinitely by mass concentrated to a point of infinite density. Here, too, however, the rules of physics break down and there is speculation about exactly goes on inside one.
If we get back to CMB for a moment, there is another way to think about why those original photons are still everywhere. Because the universe is a self-contained expansion of what was originally a singular point, there is no location in the universe that you can label as the starting point of that expansion. The entire universe is the starting point. Although scientists (correctly) talk about the oldest stars being those that are farthest away from us, it can be a bit misleading. It doesn't mean that space-time is youngest in the center, and that center is surrounded by older shells of space-time. The space-time of the whole universe is the same age. The whole universe is that point in space 13.8 billion years after it started to expand. That being said, there are older and younger stars. The oldest stars, mentioned earlier, first began to shine just a few hundred million years after the Big Bang. Thanks to the universe being a giant self-contained Big Bang, we can see almost the entire evolution of the universe just by observing photons of light. All the ghosts and echoes of the past are still there. From Earth, distant stars are moving away in all directions. They are red-shifted, or Hubble shifted. The most distant stars are the oldest stars and they are moving away fastest. This is not because Earth is in the center of the universe. It is because everything is moving away from everything. If you could jump into a wormhole and travel instantly somehow to any distant planet in any distant galaxy, you could look up in the night sky there and see the same phenomena. Distant stars would be moving away in all directions and the oldest most distant ones would moving away fastest, approaching light speed.
By mapping out the ancient CMB photons across the visible sky, scientists can glimpse what the very young universe looked like. Its energy wasn't perfectly homogenous. Those slight variations in density created tiny gravitational pockets into which matter tended to clump, forming the first stars and galaxies. Those ancient photons could not travel freely when they were first created. The universe was so dense and energetic that they constantly banged into electrons and protons. When the universe was about 380,000 years old, the density of electrons and protons was low enough that photons could travel for distances between them. From then on, they were free to travel not outward into the universe but in all directions as the universe expanded outward. That is why we can see back into the universe's past only up to 380, 000 years after the Big Bang. By observing a similar map of neutrinos, however, physicists hope to see the ghost of an even younger universe, because neutrinos escaped and began to stream long before photons could. The tricky part here is that neutrinos are themselves almost ghostlike particles. They are very difficult to detect.