When does One Piece take place?
Well, actually! One Piece doesn't even take place on earth. It's pretty obvious when you take a glance at the planet's geography:



Not even during earth's theorized pangaea phase did it ever look like this. So One Piece is either very, very, very far into the future, or more likely simply not on earth at all.

A lot of ideas in OP are gathered from the eras you've mentioned, certainly, as a thematic thing, but they don't actually take place in those points of human history.