I am writing a story, in which the greek gods appear. The main point I need is, when exactly the many greek gods such as important figures like Zeus, Hades, Poseidon, Cronos etc. appeared in history for the first time. Bascially, when did they have an cultural impact and slowly over time "lost" their meaning. It is a very big story and I am trying to be as accurate as possible with respect to the many cultures I am using. I am not well-versed in history or great at researching, which is why I am asking here, hoping some experts can help me out. It is important for me, to have a deeper understanding of the context regarding my question. Preferably in the form of books, internet sources, videos or at least based on their own experiences
Edit: This question has been previously asked on the history forum and it was decided to post it here. Another thing is, it was explained to me, that asking for sources, may not be the right approach, since they tend to be more subjectively then factually correct. Especially when trying to clarify the nature of the timeline, when greek gods played a huge role in history.