We currently have the technology necessary to send astronauts to another star system within a reasonable time span. The only problem is that such a mission would be overwhelmingly expensive.

Even with our most advanced technology, sending astronauts to another star system is currently impossible within a reasonable human lifetime. The nearest star (Proxima Centauri) is 4.24 light-years away. At current spacecraft speeds, this would take tens of thousands of years. The problem is not just expense - we lack propulsion systems capable of reaching necessary speeds and life support for multi-generational space travel.