The ball on that may have gotten rolling with the invention of Colonel Green near the end of the series and his description as being involved in a "genocidal war early in the 21st century," clearly placing it after the Eugenics Wars. Then Gene and the creators decided on a nuclear World War III for Earth sometime around the mid-21st century in the premiere of TNG so it all had to be worked together, making the Eugenics Wars of the 1990s and the nuclear Third World War two entirely separate conflicts divided by fifty or more years.