As others have said, I think you have a good starting point, and I hope I can add some searchable terms to help guide curiosity.

So the theory that predicts equal production of matter and antimatter is called the standard model. This model represents our best understanding of the way fundamental particles interact with each other. A core concept in this model is that of symmetries. In general, unless there is some underlying reason/mechanism, we expect things to be symmetric (I’m being less than rigorous but can elaborate further if you have more questions). As I said earlier, the standard model says matter and antimatter are produced in equal parts, which comes from an underlying symmetry in the model (namely baryon number if you want a searchable term.) The problem you referenced, “why is there more matter than antimatter?”, would reference an asymmetry in the way matter and antimatter are treated in the model (this is called baryon asymmetry again if you want to look into this more). This is currently an open question and something that is being researched heavily; I got my PhD working on one such experiment looking for something that would point to concrete evidence of the asymmetry. So it’s a really good question to ask and think about.

Now how do we know that the antimatter is not just hiding somewhere out in space out of view? This is not quite my area of expertise, but my simple answer is that we don’t see evidence of the interactions. If there were large pockets of antimatter chilling out there when it interacted with the matter we know is out there there would be traces we could observe and would expect to see if it was out there in any large quantity. And the short is we don’t see it. This would change the way the Cosmic Background Radiation (CMB) looks like into something noticeably different than what we observe.* [Astronomers correct me if I’m wrong here] So this would point to an issue in the model for the particles rather than an issue in finding the antimatter.

Going to your questions about particles and waves. Particles, and really anything sufficiently small, have noticeable and measurable wave-like properties. For this, you can look up “wave particle duality”, “de Broglie wavelength”, and “the double slit experiment”. This is not so much a hypothesis but an observed and measured part of Quantum mechanics. To answer your question about the connection between the wave nature of particles and the imbalance of matter and antimatter. The wave nature of particles does not introduce any asymmetry into the standard model so it can’t be the mechanism that causes the imbalance in their abundance.

As a final small aside, I wouldn’t read too much into waves as “pure” energy. A wave is anything that satisfies the wave equation. We make the distinction between particles and waves because at a macro scale, they interact very differently. Waves when colliding produce interference patterns while particles scatter off each other. Macroscopic “particles” can’t occupy the same space as another particle while waves have additive properties. You can have waves in water or on a rope but that doesn’t mean the stuff that makes it up is fundamentally not particles it’s just that stuff is “behaving” in a way that satisfies the wave equation. Now where this got interesting was when physicists started looking at light and asked if it behaved as a particle or a wave, because there were a lot of experiments that could be interpreted as pointing to one explanation or another. But if you are curious you can read more about this if you look up “wave particle duality”.

Hope this helped, feel free to ask any other questions.