Could matter have always been present

I've been pondering this question in my head so here it is:

We all know that matter cannot be 'created' or destroyed. So, if this is correct, we can logically assume that matter was never created. For this reason, could we draw a reasonable conclusion to say that matter could have always been present for an infinite amount of time, maybe shifting from one form to another?

Understandably, the leading theory for the creation of the current universe is the Big Bang Theory, and of course, it is believed with good reason, nevertheless we do not know what came before the Big Bang. Could it be possible that the Universe might, perhaps, be in an infinite recursion, and also, for the matter in the Universe to always have been here, constantly shifting in form? The gist of what I am saying is could the Universe have always been here, along with the matter and energy within it?

Before saying that "It just can't happen" or "it is illogical," present evidence to support your answer. For instance, if it breaks a law of which I am unaware.

Thanks in advance.

While the classical mechanics principal of conservation of matter is useful, it has had to be expanded to include energy. Matter is destroyed all the time, in any chemical reaction, to create energy. And conversely matter can be created. Particle - anti-particle pairs pop into existence all the time, drawing from the Universe's energy, but they always go on to self annihilate unless they are on the border of a black hole's event horizon.

But you are right in principle. There is a conservation law at work. Though through some high particle-physics wizardry it's possible the universe can create energy as it expands. I'm not sure how that conclusion was reached. Perhaps it comes from vacuum energy. It's thought that the every point of the universe if full of an incredible amount of energy but we don't perceive it because its the same everywhere. Just like a boat can sit still on a lake because there is no current.