Maybe they had some sort of throttle accident and got there via time dilation (from the crews perspective natch).
...But not from Kirk's, alas.
Regarding throttle accidents, an unused Okudagram describing what happened to the Charybdis
mentions a "thrust anomaly" that gave the ship "12× solar escape velocity 2.56 hours earlier than planned". This tells us little about whether the Charybdis
had rudimentary interstellar capabilities, as twelve times solar escape velocity somewhere in the outer Sol system would add up to only around a hundred km/s; even though it's a planned capability, it's not yet a practical interstellar speed, not even with the cryosleep systems the ship was indicated to have aboard (in this noncanonical, unused graphic, that is).
But it's indeed a "thrust anomaly" in that the Botany Bay
and the Ares
ships were apparently doing much better, somewhat earlier... Perhaps it's for the best that we never saw that graphic as part of the "real" Trek universe.