Your question (at least in the way that you have phrased it), is more of a philosophy question than a Physics question.
Let me put it this way: Why does space exist? Why do particles exist? Why does energy exist? Why does temperature exist?
Physics is trying to observe what does exist, and how it behaves. This can be done by observation, and fitting models to the observed. Answering questions about why something exists is a metaphysical question, and not amenable to the scientific method. This way lies religion: "Beause God made it that way", or "Because the back of the turtle that we stand on is curved".
Why accept Relativity?
Now as to why we accept such a theory "without a cause", the cause is that we observe the constancy of the speed of light in any inertial frame of reference. This result is simply unexplainable in our usual assumptions about velocity.
To come up with a model of the universe where we mess around with times, distances, velocities, mass etc. was not easy, and required an enormous amount of incontrovertible evidence. But, given that evidence, physics was forced into coming up with the simplest (Occam's Razor) theory that could explain the observed, and since nothing very simple fit, we had to keep getting more and more wierd, changing time and space, until the first possible fit was found (special relativity), and soon afterwards general relativity.
Even after having this model, not everyone was comfortable with it, until many more confirmations started to appear. Now there are so many confirmations (and they are shared not only in the world of Physicists, but in many mass paperbacks) that even flight plans of spacecraft include relativistic corrections.
Finally, we realize that even this complex theory is not the "Truth." It is a closer approximation than the first model, but still needs Quantum Mechanics, and who knows how much more tweaking before it is "True," or even if "Truth" can be written in a finite set of equations.