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.
The rest is in the next comment.