https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls...
An updated design from the 80ties calculated a time of 100 years:
https://en.wikipedia.org/wiki/Project_Longshot
And a nuclear fusion design is calculated to achieve 12% of light speed, thereby reducing time to reach the fourth nearest sun system in 46 years.
https://en.wikipedia.org/wiki/Project_Daedalus
So there are concepts that could make unmanned interstellar travel possible, even within a humans life span, it's just that it costs so much and the incentive is pretty low compared to the incentive countries had for getting objects into space. (primarily military incentives - get spy satellites and nuclear warheads into space to not fall back behind adversaries)
I believe that given a strong enough incentive humans could do it, no matter what current consensus is telling us.
Humans set out to work on reaching outer space without even having a design on how this could be achieved and we did it anyway.