In the first chapter, Twilight reads a journal dated November 23 1962. I think it's a pretty clear indication and it corresponds with the period during which germany was divided in two.

Overall and from what I've seen, the show does a decent work keeping track of the correct tech, but there are a few anachronisms I noticed. Like how Loid says he's going to record a TV show on tape or the use of Heinz ketchup, both things weren't invented back then. Or the fact that the fake spy show Bondman is wayyyy too high quality compared to what cartoons looked like back then.

We went from a cheesecake image to discussing the time period the series is set in. Never change, KYM