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Initially, my assumption was some form of prophecy. Nothing mystical, but perhaps an older form of man had knowledge of both beasts and assumed if they crossed paths the death toll might be apocalyptic. Hence all the skulls, falling bodies and flames below them.

But, the more I think about it the more I like the idea that they've crossed paths before. It already establishes them as enemies and King Ghidorah needs to come off as a grand arch-nemesis for Godzilla.

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Think I'll be a complete fanboy when I say this but, the Shobijin did the cave painting? Think about it...Godzilla vs. Mothra 92 saw cave paintings of a battle between Mothra and battra, and Godzilla final wars 2004 we saw cave paintings of a battle between Mothra and gigan. 

All seem to point to a previous battle or even a prophecy battle. Right now, it's in the air. 

I think it is both. I think Godzilla and Ghidorah met in the past. They fought, Godzilla won, Ghidorah retreated back into space and is planning on returning when he thinks he can win.

Given how our ancestors likely worked on a cognitive level, Godzilla and King Ghidorah most likely did tussle in the past, and happened to be observed by these ancient humans.

How ancient, who knows? It's possible that Godzilla only surfaced at that point in history specifically because an invader and threat to Earth's balance showed up.

And yes, I AM going with the idea that King Ghidorah came from space.

I'm betting that many years ago, Ghidorah rose up/came to Earth, and Godzilla, Mothra and Rodan battled him - explaining why they were on the cave walls. Eventually, Godzilla defeated Ghidorah (as shown by the paintings), and the dragon retreated. Then the three returned monsters returned to their slumbers. But in 2019, Ghidorah returns, so that triggers the three to come back. 

Think like the IT movie. The kids defeated the clown, but when he returned they came back to defeat him. Just imagine that but the kids are Godzilla, Rodan and Mothra and the clown is Ghidorah.

^Nice.

What if the Ghidorah in the cave paintings is a different one? I mean, if Ghidorah is going to be an Earth kaiju, it would only make sense that there would be other members of his species, and if Ghidorah is an alien creature/organism/parasite, there may be other kinds out there as well. Just an idea perhaps? 

I think both

 If they crossed path before, that'd be consistent with the previous Japanese versions.  I like to think that ancient people had seen that they appeared in separate periods of time and wrecked havoc multiple times previously.  They also confronted each other and fought but were spent in their battles, so they each retreated to recuperate.  That does not contradict with what we saw from previous Godzilla films, and is also consistent with what people from Monarch were saying that Monsters really existed and owned the Earth, not humans.  They will appear when there is a loss of balance on Earth, for good or bad, to restore the balance there, even though humans don't appreciate their so-called 'destructive' methods.  Due to radiation and pollution levels rising as well as global warming getting worse, they re-emerge from hibernation, perceiving what humans are doing is jeopardizing their food sources, to teach mankind a lesson, and of course when they will finally face each other through their own instinctive hunting habits, battles and destruction on a scale never seen before will erupt!  This time they will pack a lot more punch since they will grow even bigger and stronger!

I'd like to think that Ghidorah is a much mutated form of a MUTO. I dunno why. I wanna see him have mandibles for a lower jaw and MUTO heads and wings. I think it's kinda cool. But if they go for a draconic Smaug look, would probs be better. Of course a long neck should always be there for Ghidrah, and gold skin. But eh, seeing him have his usual stance seems so, not realistic.