It is **never suggested** in *The Original Series* that Kirk's Enterprise (or that the generation of explorers that includes Kirk and his crew) are the "first ones" to explore deep space.  It is also **never suggested** that warp technology is a "new technology".  In other words, nothing in *TOS* contradicts the existence of previous generations explorers who have access to warp technology.


Indeed, the episode ["Balance of Terror"][2] reveals that United Earth had once fought a protracted war with the Romulan Star Empire decades before the time of *TOS*, leading to the establishment of a Neutral Zone between their respective domains.  The fact that humans could efficiently reach the location that became this Neutral Zone implies that warp technology was available well in advance of *TOS*.

![enter image description here][1]




  [1]: https://i.sstatic.net/zKbUD.jpg
  [2]: http://en.memory-alpha.wikia.com/wiki/Balance_of_Terror_(episode)