We are actually sure, I'll tell you how.
Start with e=mc2. This has been accurately measured as true.
First of all notice the c (speed of light [speed of the universe]) in there.
People always talk about how things get heavier when they go faster, so why is that? It's not a magical property of the universe, it's simply e=mc2
As you go faster, you have more energy. Since you have more energy you are heavier. Now if you want to go even faster you also have to accelerate that extra mass (energy) as well, so you need even more energy.
Do that over and over and you get the famous relativity equations. You find that as you get closer to c your mass goes to infinity.
This is probably not enough to convince you, but I'm not done.
This formula was not discovered first, and then relativity from it. It was the reverse.
It started from noticing that no matter how fast a distant star was moving (two binary stars orbiting each other), the light always moved at the same speed.
Start with that assumption, and create rational formulas to explain how that could work. They are called the Lorenz transform.
Calculate what happens to mass as it undergoes the Lorenz transform and e=mc2 falls out of the equations.
If there was a faster speed possible the Lorenz transforms would work differently, and e=mc2 would be different - but we know e=mc2 is correct. And we've also measured parts of the Lorenz transform as correct.
Look for the book: Relativity, the special and the general theory: a popular exposition by Albert Einstein. Sunheading: A clear explanation that anyone can understand.
The whole set of formulas is very self consistent, if any one part was wrong (and we tested many parts) the rest would be wrong too.
The final question is, ok you can't send matter faster than light, but how do we know you can send a message faster than light? It's because information has an energy content. Each bit of information is equal to a small amount of energy. So if you send information, you are sending energy.
As a side note, tricks might be possible, i.e. don't take the long route through space, but take a short cut. This could work if the universe is curved (curved in 4d), but current thinking is that the universe is flat. In the book I recommended Einstein talks about how to measure if the universe is curved or flat. (For a 3d example it's going through the earth, instead of on the surface.)