The premiere of "Waiting for Godot" was the 5th of January 1953 in the théátre de Babylon in Paris. (originally in French, that´s why) With the use of this information I´m taking a chance by saying that also in "Waiting for Godot" the time period will be the same. Approximately 1953.

The time period is important for understanding the kind of language which is used in this play and also explains the clothes which the characters are wearing. (cylinder hats etc.) 

As I read on I understand the main theme of "Waiting for Godot" is that people are all the time waiting for something or someone. Yes, in this play the main characters are waiting for Godot - God but I believe there is a deeper meaning. It´s not about waiting for God, it´s about people and society. The fact that people are waiting for something all the time and usually don´t take any action to solve the problem themselves. Just like in the play when they say something like; "Let´s wait for Godot to decide." By this nothing will be sorted because Godot will never come and thus the cycle starts all over again because people are usually lazy to take their destiny into their own hands and do something. This is something I have personal experience with because I myself see this behavior in everyday life.
By this post I want to say that I strongly believe this play is still relevant and will be for a long, long time......