I don't fully understand your example. If you're just talking about small vehicles taking years to reach another solar system, then I think a launch like that could happen soon, like in the next century or two. There would have to be breakthroughs in propulsion. I'm talking about a vehicle with actual functionality, with GNC and comms to earth.

I think we will never be able to exceed the speed of light. It's just a fundamental hard reality of spacetime. So, for practical purposes, humans will never reach other star systems like in science fiction. Of course, there are ideas for generation ships that take decades or hundreds of years to reach other stars. I think something like that is far off, maybe never.