Prior to the collapse, we know Maya had planned to resign from her post at Lhasa, (where she worked on what later became the War Cult's future-viewing machine,) so that she could rejoin her wife, Chioma, at Hyperion. We also know from her journal that she, along with Rasputin, identified the need for something 'not human' to cope with the rigours of using the SxISR. It's likely that this was the trigger for the development of the human-to-Exo conversion program at Clovis Bray, something described in Cayde's journal, (who also reminisces regarding his time working as Maya's security, seemingly post-conversion.)
So here's the thing. In the secret area of Cayde's Stash, he recalls having had a sweetheart of sorts, who he references using the Royal Hearts cards in his suit system. His journal references to a crush he had on Maya immediately come to mind, except... He can't remember that. Or certainly shouldn't be able to clearly, since it was pre-collapse, and none of the Exo's can clearly recall anything pre-Collapse.
Or can he?
My theory is this. Maya, Cayde, and potentially any number of others who worked with Maya at Lhasa, somehow survived the collapse. Perhaps, given Maya's description of SxISR as a mimicry of the Vex Gate tech that she, Chioma, Duane-McNiadh and Doctor Shim played with at Ishtar, she somehow used it to escape into the Vex network, and back out again afterward. The fine details aren't necessary, except that in tandem with her assertion that deeper use of SxISR would require 'something more than flesh and drug,' than that achieved by the test subjects, it's likely that she would have needed to Exo herself to have used it in this fashion. I'm of course presuming a copy of someone's mind can be written back onto an Exo. We know they had the technology to make the copies, (Maya, Chioma, et al are seen to have done so in prior gimoire entries at Ishtar,) but whether than copy can be written to anything after is debatable.
However, if we now work on the presumption that this was a thing, it makes sense for Maya, as the Exo Stranger to have been the one to turn Rasputin back on. Why? Because everyone else that might have had access to do so would probably have been long dead. Or certainly in no position to reach the bunker. During Ghost's examination of the console that reactivated Rasputin, he mentions the constant reuse of a retinal scan, and the likelihood of that scan having been completed with 'preserved tissue.' Perhaps part of Maya's human legacy?
Either way, if Cayde was with Maya during that initial visit to Rasputin, and then met his demise and was turned into a Guardian after, it might go some way to explain why had an override code to Rasputin's bunker. He states in his journal that '...the reboots, they dont wipe it all away. Not everything.' Perhaps he recalls the code from that trip, although not the details of the trip itself? Maybe he then used it to raid Rasputin himself afterward, perhaps in part, trying to recall more of his past. He does seem rather philosophical in his journal entries, behind the bold camaraderie. It may also be that he's romanticising the feint memory of Maya as having had a sweetheart in a prior reboot, rather than actually knowing and remembering having had one, and has a personal ritual of setting aside part of his stash in honour of that memory, on the off chance that he one day bumps back into her.
The bottom line, however, is thus: the Exo Stranger states to the Guardian that she isn't 'born of light,' yet it's clear she has abilities not considered 'normal' by Ghost, who is quizzing her. If she's a pre-collapse Exo who has use of SxISR/Vex Gate technology, then she would be appropriately different to spark Ghost's interest.
Maya, or one of the 227 copies of Maya's subconscious uploaded into the Vex network at Ishtar, and then downloaded into an Exo frame, seems like an appropriate individual. She's one of the people to have used the machine to know the collapse was coming.
tdlr logic dump from discussions elsewhere:
[spoiler]- Cayde was an Exo, pre-collapse.
- Cayde knew Maya, as an Exo, pre-collapse.
- Cayde can remember Maya, post-collapse.
- Ergo, Cayde cannot have experienced the collapse, (Re: Exo lore.)
- Supposition: Cayde was in the machine during the collapse.
- Cayde was with Maya at the machine facility with Maya, pre-collapse.
- Maya was part of the team that could operate the machine.
- Cayde does not mention anyone else from the team, post-collapse.
- Supposition: Maya was the one who took Cayde, (and whoever else,) into the machine during the collapse.
- Ergo, Maya had to be an Exo by then.
- Maya worked with Rasputin, pre-collapse.
- Organic material was used in a retina scan in Rasputin's bunker, following the collapse, to wake the facility up.
- Supposition: anyone not in the machine during the collapse with military/scientific clearance is likely dead.
- Ergo, Maya woke Rasputin.[/spoiler]
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I'm coming to the party late, but you said, "We know they had the technology to make the copies, (Maya, Chioma, et al are seen to have done so in prior grimoire entries at Ishtar)" and I don't think that's the case. I imagine you are referring to Ghost Fragment: Vex 4, "Maya, Chioma, Duane-McNiadh and Shim decide to have a picnic before they send themselves into infinity."?? Those 227 copies of themselves we made by the subject 12, the operational Vex platform in the first Ghost Fragment: Vex. Maya may very well be the Stranger as well and its an intriguing idea. Regardless I'm pretty sure the Stranger, whomever she turns out to be has a very important role in Destiny's future.