Nolan confirmed in a behind-the-scenes video that Westworld was set in the 21st century, so it’s certainly a timeline that makes sense.
A brief landing page at the beginning, however, holds an important detail.
Still, the series has a proven habit for eschewing linear narratives, so it’s possible we’ve watched scenes from across the century (or centuries, as the case may be).
According to the date seen in the top left corner of the screengrab above, Maeve’s escape occurs on June 15, 2052 — roughly 36 years into the future.
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Welcome to Westworld | About The Series - Westworld (HBO)