I suspect that Archer begins somewhere in the 1990s. This theroy is based on the weapons used and shown in the show. Cellular phones are also an indicator of the timeline, one of wich is a slide type phone. The first such phone was released in 1999. But these are just assumptions. I personally place the show's timeline 1999 and 2005. But then theres the KGB, a Soviet entity, that is called FSB today, because of the 1991 regime change in Russia. The Tec-9 is an iconic 80s gun. The clothing worn by the caracters, especially Lana Kane, has been worn at many times in the 20th century. Suits like Archer's date far back to the 19th century. but Lana's long boots and tight wear looks more 80s than the clothes worn by the male caracters. 

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