See The Expanse if you want to see this in action at speeds significantly less than c.
Edit: Even for just getting around in the solar system, they had to magic up some chemicals to allow the human body to withstand deceleratory g-forces strong enough to keep travel times short enough to not completely wreck the narrative.
Acceleration at one gravity is 9.81ms-1 which is about 35km/h per second. That would take about a year to reach close to the speed of light.
You’d then need to spend the same amount of time slowing down.
So to get to our nearest stellar neighbour (alpha centaurii 4.3 LY distant) you still need to coast for about 2.3 years in the middle of the journey.
This is all assuming you can provide that much thrust constantly for two years.
We just need to discover astrophage.
See The Expanse if you want to see this in action at speeds significantly less than c.
Edit: Even for just getting around in the solar system, they had to magic up some chemicals to allow the human body to withstand deceleratory g-forces strong enough to keep travel times short enough to not completely wreck the narrative.