I always thought it was cool that with Star Trek (original series) that their future was roughly 300 years ahead of the 1960's. And since over 50 years now have passed since the original series, that future is only 250 years away. If medical breakthroughs happen in our lifetime, such as ending and reversing the aging process, it's conceivable that either our generation or the one after us could possibly live to see the years Star Trek is set, "in roughly the 2260's". Or possibly the nearer future of characters like Zefram Cochrane (who in the "Metamorphosis" episode created the space warp engine, and again appeared in the Star Trek: First Contact movie, set in 2063 ).
And the Star trek: Enterprise series set about 100 years prior to the original series, in the 2100's, is a part of the Star Trek early future we might have a chance of seeing.
Interestingly enough, we're already about 25 years past TOS's "Eugenic Wars" in which Khan was ruler of approximately (IIRC) one-third of the planet before being banished into space. In the original timeline, Khan ruled in the early to mid-90s.