Ronald Held wrote:
I see no problem that Cochrane had a team build the first warp capable ship and had most of the work completed before WW III. Perhaps the war slowed but not completed stopped the project?
It's possible that America had little or no involvement in the third world war.
While there was a sighted example of Lily having trouble obtain a certain material (titanium), the missile complex in Montana was still there, and Cochrane was able to travel by train. Rail tends to pass through population centers.