Does the CMB contain any clues to what caused the Big Bang? Does a mathematical model theorize it?
Caveat: I'm not a cosmologist, so this answer may not reflect the forefront of scientific knowledge/accuracy, but I have some knowledge so thought I'd share it and hopefully someone can correct me if I'm wrong.
The Big Bang theory states that everything is moving away from everything else, so it must have started closer together. We know from the Cosmic Microwave Background that everything was very dense and hot and small.
You may have heard that the universe started in a singularity. This means one point at which all matter was in the same place. In this state, all information in matter is lost. No particle can be labelled as having a position or size or spin, because every particle is in the same state as every other particle. This means we lose all possibility of having any information about what happened before this. There are many theories of what could have been before this, but no matter how simple/beautiful/mathematically rigorous the theory, it is physically impossible to know anything about it so they are impossible to test. In some definitions this makes these theories not actually science, as the scientific method involves making testable predictions.
We don't really know what happened before the big bang, but it is logical to think that just like the the mass was released when the big bang happened, it also got crushed to that single point, and since energy can't be created or destroyed, there was also mass before the big bang. And this is also a lot similar to a black hole, leading us to think that the big bang might have been a black hole