OK, so I am probably not the first person to say this, and I haven't read all the hundreds of forum comments yet, but all this talk about alternate timelines has compelled me to present an alternate argument. :) this is one of the more interesting aspects of Westworld to me intellectually, or from a sort of "literary analysis" perspective, and I think all this tinfoil about multiple timelines gets it kind of wrong.
OK, so Westworld the show has a really unique narrative structure. I think people are just using their bicameral minds (joke, I know I am not using this properly) to interpret this as multiple timelines, but I don't think there's any evidence of "multiple timelines" in terms of calendar or clock time, and here is why.
1) We have alternate narratives in Westworld that are playing out in the same (probably) physical space: The narratives of hosts and the narratives of guests.
Hosts are robots that are programmed to perform a loop. We have seen evidence that the hosts' loops can span a day, a week, or a longer period of time. We have seen that hosts reset and play out the same loop over and over (Delores waking up and greeting her father in the morning, Teddy riding the train). We see that events in the park can interrupt their loops and even change their course. The hosts are not supposed to be aware of their loops, and at the beginning of the show the main hosts we see do not seem to be aware of their loops or that they are on a loop. But their narrative timeline is not the same as a human lifespan. It's this day, week, month or whatever loop. They were never babies. They will never get old and die of old age (unless someone writes that into their storyline). Even death doesn't stop the loop. They die and their loop just starts over.
Guests are human and when they are in real life (not Westworld) they are just following a normal human timeline in terms of time and space.They were born as babies and will die at some point; maybe they will die of old age, maybe they will commit suicide, maybe they will have a bus accident, or maybe they will have a tumbleweed accident in Westworld, haha. When they are in the park, they actually do have their timelines somewhat interrupted because they are aware that they can jump in and out of these loops the hosts are on. But it's not that they are on completely artificial timelines - The sun still rises and sets and conceivably they still have to go home someday.
So, point 1, the hosts and guests are already operating on different timelines although they are occupying the same space physically. Hosts have artificial engineered timelines that repeat on various length loops and guests have mainly human timelines that are somewhat disrupted by the nature of the park and the meta-awareness of narrative loops they can jump in and out of. And then we as viewers are presented with narrative challenges we don't see in many shows, like characters dying and then appearing again in another scene as the same or a different character. And we see narratives playing out differently in different iterations because of the impact the wild cards, the guests, have on the park. So there's some cognitive dissonance built into narrative timeline, but it's not because the show is presenting two timelines in two different decades or something.
2) The hosts' perception is an engineered thing created by the employees of the park (or "someone" yet undetermined). Even though the show keeps teasing us that they might be becoming sentient, there is evidence in each case that shows someone is controlling them. For example, Abernathy seemed to go bananas and wanting to go after his creator (Ford) but it just turned out to be a garbled script. The guy who bashed himself with a rock, turns out had some kind of remote control device in him. Delores seems to be following some kind of independent path, but it turns out to be a voice in her head that could be Bernard, Arnold or someone else. The mystery of what's going on with Maeve has not yet been solved, but we already know that Arnold purposely tried to create sentient hosts and what? Failed? Was stymied by Ford or someone else? The code is there. Every mystery in terms of their cognition or behavior so far has been explained by technology.
The larger point I am making is that when we see robots as characters with POV, the POV we are seeing is engineered. Even if you think the robots are becoming "sentient" and they are having cognition that their creators didn't intend, they aren't human. They are technology gone awry in that case (or not, if it's Arnold's code or someone with Arnold's views controlling them now). So if the POV is engineered, couldn't the POV be manipulated? Or malfunctioning? We already know from when Abernathy saw the photo of the woman he found on the ground, that Delores said "it doesn't look like anything" but we don't know what she saw or what she's engineered to see or what she's engineered to react to. If someone's controlling her actively they could easily manipulate her to see herself when she's not there. If someone's code went awry it could be that when we see things from her POV we are not seeing the whole of the scene in front of her.
2-a - We know there are several characters who are park employees at different levels who like to tinker with things against their boss's wishes, which is only normal and natural for people who are engineers of different stripes working in an isolated area with nothing to do with their free time and working on this unique technology.
3) brings 1 and 2 together- The concept of memory was recently introduced into the hosts' code and caused a bug. The park thinks it recalled the affected hosts and wiped the bad code, but anyone who knows anything about software knows that when you write some sophisticated code and cause a bug to happen, it sometimes happens that you don't understand where the bug was and it can be harder than you might think to roll it back.
So the concept of memory has already wreaked havoc on the park in terms of: The Milk Bandit who killed everyone who killed him in previous loops. Abernathy who appeared to go bonkers when he was just jumbling up his lines from an old script into his current storyline. Maeve remembering an old storyline with a lot of death and destruction on a ranch. The intent, as I understand it, was to only let them have a tiny emotional hint of these memories to spice up their emotional affect, but what happened was it was way too intense and so their emotional affect went bananas.
We also see the hosts can be implanted with artificial memories, like when Ford implants Teddy with the memory that he was a soldier who served under Wyatt until Wyatt went nuts. The show presents this narrative as a flashback, but we know it's not because we know Ford just recently implanted it in Teddy to spice up his narrative.
Conclusion: Unique Narrative Structure, not Multiple Timelines
So the stuff that happens with Delores (and other characters, but I am just going with Delores as an example) where she pops in and out of scenes with others, where she sees things that aren't there a second later, sees copies of herself, and can do things she's not programmed to do, could be a mashup of memories of former storylines, code that was written by Arnold, we know Bernard messes with her too, we don't know what else has been done with her by other tinkerers on the staff, and we don't know who might be manipulating her now or if she's being manipulated by someone who is stealing the park's data (like is she one of the ones with the device in her arm?). This, to me, is the central mystery of the show, that I'm waiting or not waiting to find out depending on how much I decide I care. But I think this unique narrative structure and multiple layers of "reality" that's been sliced and diced in different ways has created this idea of "multiple timelines" that I think is sort of beside the point. There are obviously multiple timelines in terms of narrative and perception but they aren't " differnet guys in different decades" IMO.