It’s not too far in terms of human lifespan, but with current technology it would take approximately 17,000 to over 70,000 years. One light-year is the distance light travels in one year, which is about trillion kilometers or roughly 63,000 times the distance from Earth to the Sun. Voyager is about 1 light-day (~24 light-hours) away. That means it is moving at approximately 1/12,000th the speed of light. Still very fast relative to us, but very small compared to the distance of a light year.
Since interstellar travel isn’t feasible for the current technology, we would need a breakthrough in engineering to increase the speed traveled by our spaceships to have any hope of ever reaching another star system.
It may be possible to one day harness the full capacity of nuclear engines, which could boost the velocity travelled up to 7.6% of the speed of light. These are called Nuclear Salt Water Rockets (NSWRs).
Even travelling at 7.6% of the speed of light, it would take about 55 years to reach Proxima Centauri, our nearest star, 4.24 light years away. Considering the galaxy is 100,000 light years across, it starts to sound implausible that we could realistically explore our universe. Granted that time slows down due to relativity for those in the spaceship, even at relativistic speeds time doesn’t slow down completely. That would require an infinite amount of energy.
There are other technologies or phenomena we could potentially use if we figured out how. Displacing space around the space shuttle (sci-fi warp speed) or wormholes. There are other potential technologies like laser-propelled light sails, which could reach 0.2c or 20% of the speed of light. However there are engineering barriers here, such as keeping a steady and strong enough beam, requiring a 100-gigawatt (GW) power source, of light to the spaceship. This energy output is equivalent to the output of roughly 100 large nuclear reactors
Nevertheless there are backers of this technology, like the Breakthrough Institute hoping to, for example, reach Mars in just 20 days.
Travelling at 0.2c means that for every hour on board 1.021 hours would elapse on earth. If somehow you could make it to extremely close to the speed of light, you would effectively not age even covering vast distances. We are obviously a long way from that, but without relativity we would have no chance of ever being able to visit other habitable planets, let alone star systems.
I mean, there could potentially be cryostats in the future, but that is wrought with other problems, such as the high toxicity levels induced on the body to effectively freeze a human at the temperature required for long term space flight. Maybe one day someone will invent a safe way or alternative, but until then other types of spaceflight technologies are likely to be the best chance of reaching other star systems.