You don't need to break the speed of light to get to the stars. Time dilation and space contraction mean that you can get there in as little time as you desire.
Everyone you knew on earth would be dead by the time you got back, but if it's just about you, the speed of light is no limitation at all. (The rocket equation, however, presents stupendous engineering challenges.)
>but if it's just about you, the speed of light is no limitation at all
It's a huge limitation, even just getting propelled to "big enough speed", say 1/10 the speed of light.
We barely do 1/1500 the speed of light, in unmanned probes, and only because we sling shot on Solar gravity, not as propulsion or anything, and at 1400 o Celcius, plus deadly radiation, not to mention any micro-meteor as big as a particle of dust could kill someone there).
Don't even need to do time dilatation - just make you lifetime longer by techjlnical means (ideally almost infinite) and you will be in the next star sumystem before you figure out how to exit your VIM session.
> Time dilation and space contraction mean that you can get there in as little time as you desire.
This is confusing science fiction with physical reality. See e.g. https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/... for a reality check.
Time dilation and space contraction only matter if you can reasonably achieve speeds of a significant portion of the speed of light. AFAIK nobody has even come up with a reasonable way to achieve this for lightweight probes, let alone for hundred-ton ships capable of carrying humans. And let's not forget the practical problems like all photons incoming from the front being blueshifted into ultrahard radiation that would make a point blank nuclear bomb seem like a small candle.
Realistically even getting to the nearest star in less than 400 years experienced time is way way WAY out of reach for now.