This is the big probelm.
By the comments in this strip and the ones following it, the GG were given to Tepoz shortly before the attempt to destroy the Calendar by May. That was around 562. If this is right then how could the girls be under Tepoz's control 5000 years earlier? If that date is correct then any other time line kinda doesn't make sense. I agree there have to be things we don't know yet but this is a pretty big time gap.
My guess is that Bud is talking about two different (but related) times and events here:
- The time/point at which the Timekeepers (including Mayahuel) transferred the GGs to Tepoz. At that point they were making plans to destroy the Calendar Machine.
- The time/point at which Mayahuel actually attempted to destroy the Calendar Machine, was tossed into the Demon Dimension, and the time loops started.
I don't think these are one and the same. Bud's comment about "you went looking for her" implies quite strongly that Jin had been sent away, and was coming back to try to find Mayahuel... and found her just as May was trying to destroy the Calendar Machine and was tossed into Tumbolia.
We seem to have two conflicting scenarios here.
In the first (yours) Tepoz received control of the GGs quite late (around 562). The problem I have with this hypothesis, is that it seems to be incompatible with lots of other parts of the story as told. Bud made it fairly clear to Monica, early on, that the GGs were not truly individuals at all before Tepoz took control of them... their personalities and memories were still mash-mingled together and spread across all three bodies... the Timekeepers had separated the Chimera out into its constituent three golems but had not cared or bothered enough to finish the job of restoring them further. Hence, Brandi and Acacia couldn't possibly be acting as they have been shown this week (Brandi is clearly a distinct individual... actually, two of them). We know that Bud was present at the court of Amenhotep IV in Egypt, and apparently did something she is now somewhat embarrassed about... which implies that she was an individual at that point rather than being just one-part-in-three.
In the other scenario, Tepoz received control of the GGs thousands of years ago, disentangled them, and brought them over to the New World at some point (some time before the Olmec civilization was founded, it seems). They had some degree of autonomy at that point. Some thousands of years later, Jin searched actively for Mayahuel and found her just in time to lose her again. This scenario is consistent with what we've just seen happening in flashback at Mapimi - at the time of the Kikai Caldera eruption, Brandi and Bud were individuals, but Bud (at least) had not had all of her original memories restored or released.
This second scenario requires (I think) the "two separate events" interpretation I wrote above... Bud is actually referring to two different times, with a long interval (thousands of years) between Mayahuel and the Timekeepers planning
to attack the Calendar Machine, and Mayahuel actually doing so.
Why Mayahuel waited as long as she did... uncertain. My guess is that she held off in the attack because she knew how thoroughly well defended the Calendar Machine was. She may have finally tried it out of desperation, or out of a mistaken belief that she knew how to overcome its defenses.
To me, it seems that the "early Tepoz handover" scenario has far fewer possible inconsistencies with the total story as presented.