Yes and it won’t be that far in the future as one might think and the reason is…
Fusion power - the same process that happens in the sun where smaller molecules are merged into bigger one’s, generating extreme amounts of energy and creating matter which can be expelled at high speeds to propel a spaceship to close to relativistic speeds (5–15% speed of light).
There would be some challenges that we would need to overcome, such as finding a way to mine aprox. 50.000 tons of helium needed to fuel such a space craft. But that we would be able to get from, for example, a base on the moon.
Then we would need to find a way to shield the craft from interstellar dust, because at relativistic speeds, a grain the size of a corn would cause massive concussive force but that could be solved by magnetic fields combined with a regenerating physical shields (nano tech?).
Also we would need to have a system to keep people alive for decades, as that is what it would take to reach the closest star but, with bases in space and on the moon, we would have already solved that.
So, assuming mankind (or AI) does not destroy itself, I think it would be achievable in the next 50–100 years.