Well sure, it's growing in popularity if you consider it's been around since the 1920's. Its main decade of growth in popularity was the 1930's, when proof of it finally began to come in; it was in the 1930's the Einstein was finally convinced of its validity, due to the work of Edwin Hubble. These days, almost all of the proof we need for it, is already in. So if the number of people who believe in it has grown from 98% to 99%, then I suppose you could say it's growing in popularity.
In reality, the Big Bang Theory is not just one theory, but a family of theories. These days the version of the BBT that is most popular is not the same version that was originally proposed by Georges Lamaitre back in the 1920's. We've learned new things about it since those days, so the original theory has been expanded and modified. These days, certain details about it are up for debate still, such as whether a growth spurt happened fractions of a second after the BB, called Inflation. This growth spurt would've happened at faster than the speed of light!
Also new discoveries, such as Dark Matter and Dark Energy, have had to be accounted for within the theory, which weren't in the original BBT. Again, this is due to the fact that we're discovering new things, and we're having to modify the theory to account for it. Science is not like religion, we do not set one rule, that must be obeyed forever into the future! There's no dogma to it, just a lot of incoming knowledge in progress.
"but the law of conservation of mass, which is a basic scientific principle, states that matter cannot be created nor destroyed. "
Okay, let me stop you right there. That is actually not a principle anymore! As I said, knowledge is constantly incoming, and we've learned a lot about the nature of matter since that principle was first stated. The conservation of mass as a principle was valid only until the beginning of the 20th century. Then we began to discover nuclear energy, and our measurement of mass became much more precise than ever before. These studies began telling us that mass can actually be created and destroyed! The problem with high school physics is that it is deliberately telling you some simplifying lies. High school physics is actually teaching you a version of physics that was around about 150 years ago, so basically around the time of the American Civil War, that's the state of the art knowledge we had of physics.
I'm sure you've heard of Einstein's famous equation, E = mc^2? What that equation basically is telling you is that mass can be converted into energy, and vice-versa. In fact, it's not just a conversion, mass and energy are different versions of the same thing. So what we were discovering is that during nuclear energy reactions, we find that a small amount of mass goes missing. That mass that's missing happens to become the energy of the reaction that we harness for our own use. It's a small amount that goes missing, less than 1%, but we now have the technology to measure minute differences in mass, which wasn't around prior to the 20th century. This amount of missing mass also corresponds exactly to the E = mc^2 energy equation.
So yes, mass can be created and destroyed!