The Past
There are characters that NEED to be related to specific dates. The Justice Society, for example, is always associated with World War II. There will therefore be a separate timeline giving the sequence of events associated with actual dates. The characters that exist within this timeline will not cross directly over into the ongoing 'number of years ago' timeline that represents our current ongoing continuity, unless there is some sort of temporal event disassociating them from the first timeline and into the second. It'll make sense as it happens.