Three chapters into Undead Unluck, and we get a specific date... August 5th. Coupled with the fact that it's stated to be in three days, this means that the manga begins on August 2nd. Will see if there's a specified year, though considering the anime uses 2020, it might be the same in the manga.
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TL;DR, timeline ATM is as follows (barring flashbacks):
August 2nd, 20XX (Chapters 1 to 3): Fuuko and Andy meets for the first time, fights Void and Shen, with Void dying and Shen telling them how to join Union.
August 5th, 20XX (Chapters 4 to ?): Fuuko and Andy arrive in Russia, fight between them and Gina (the Union member Shen tells them about)