I guess one issue is how we would say that a nothing in the past would be like a nothing here and now that we are familiar with.
As I've explained to you before, if the theory correctly describes how the physical world behaves today, and correctly predicts the results of experiments we do today; and if it also correctly predicts what we observe today when we apply it to models of the past in which we assume the physics was much the same as today, but it fails to correctly predict what we see today if we apply it to models of the past where we assume the physics to be different - then it's reasonable to suppose that past physics was much the same as it is today. It would be very hard to explain those results in any other way.
They can be wave like.
"A central concept of quantum mechanics, duality addresses the inadequacy of conventional concepts like "particle" and "wave" to meaningfully describe the behaviour of quantum objects."
https://www.sciencedaily.com/terms/wave-particle_duality.htm
Yes; they're neither classical waves nor particles, they're wave-like excitations of quantum fields, but depending how we choose to measure them they can appear to behave in a particle-like or a wave-like manner.
Since the quantum world is not fully understood now, it seems reasonable to say that we would not understand how it would have been before a universe theoretically existed.
We know very precisely (i.e. with mathematical precision)
how it behaves, but not
why it behaves that way; but this is true of other effective physical theories too. We obviously can't know for certain if it behaved the same way prior to the universe as we know it, but we can try the same maths in various scenarios and see what results we get. The various hypotheses of how the current universe came to be are the results of such exercises. If a particular scenario doesn't predict a universe like the one we see, then it's clearly unlikely to be the one that produced it.
Looking at what I posted earlier today, it seems that annihilate might not cover what happens to virtual particles? Or are you thinking of some other context?
It's just a word for two complementary particles 'cancelling out' each other. In a wave description it would be 'destructive interference'.
That is a leap of faith to imagine the universe popping out of nothing due to some remote possibility that an unlikely large quantum fluctuation in the nothing that existed.
Not really. Given enough opportunities and enough time, the probability of even highly improbable events occurring approaches 1. Your chances of winning a lottery might be millions to one, but if you entered millions of lotteries millions of times, you'd be almost certain to win one. Quantum fluctuations occur at subatomic scales and on the smallest possible timescales, so, given cosmological temporal and spatial scales, even the most remote possibility will eventually occur. You may not find it aesthetically satisfying, but - as generations of gamblers have discovered - probability and statistics in the real world don't necessarily conform to our desires or intuitive expectations.
Add to that the reality that we have no real idea even if the quantum realities in the nothing era were the same as now.
If we assume they were, the maths can predict scenarios that give rise to a universe like ours. The challenge is to find testable predictions of a particular scenario that can uniquely identify it as the most promising candidate. To go further than, "It could have happened like
this", would take new discoveries.
Predicting based on tracing things back assuming the same realities, and of course...no God or creation. In other words...religion, not fact based knowledge.
That's not what religion is; and it is fact-based knowledge in as much as assuming the 'same realities' applied in the past gives results consistent with what we observe today. If the 'realities' had been significantly different in the past, we could only get results consistent with what we observe today by arbitrary manipulation of the maths to correspond, and there's no reason to suppose that might be the case.
One can imagine all kinds of possibilities, but you need reasonable criteria of 'merit' to distinguish between them - the criteria of abduction: testability, fruitfulness, scope, simplicity (parsimony), and conservatism (coherence with existing knowledge). If simply assuming the same rules applied in the past works, then that model would outrank models that assume otherwise on simplicity and conservatism, even if all other criteria were equal - which they aren't.