They existed. Prior to the flood. One of the reasons God sent the flood.
There isn’t even agreement about that, since the term was transliterated as “giant” in the Translation of the Seventy and has often been carried on from that. The term is also taken to mean “fallen ones”, and sometimes interpreted as “fallen angels”.
Ancient peoples interpreted fossil forms as mythological critters — mammoth skulls as cyclops, some dinosaurs as dragons, for two — making up an explanation that lay within their frames of reference.
Given the implausible (and widely variant) characteristics of nephilim, and Josephus’ description, the same goes for them, ancient interpretations of fossils.
So, no, they didn’t exist.