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The problem isn't so much that humans cannot sustain high G forces for any extended length of time: The problem is that rockets cannot. If a rocket could sustain 1 g acceleration for a bit over a day, we could go to Mars in a bit over a day. It instead takes several months to get to Mars because the rockets used to get there only fire for a few minutes. The spacecraft then coasts all the way to Mars. Just a few hundredths of a g of sustained acceleration would cut the trip time to Mars down to a week or so.

The chemical engines currently used to propel spacecraft on interplanetary trajectories coupled with the tyranny of the rocket equation are the key reasons rocket cannot sustain high accelerations for an extended length of time. There are some promising low thrust / high efficiency (high specific impulse) technologies such as ion thrusters that might help humans get beyond the Moon. Ion thrusters are in use now, but none are quite ready for prime time when it comes to human spaceflight. There are some promising high thrust / somewhat high specific impulse nuclear technologies that might be useful; these are mired in politics.

Other than science fiction, there is no known technology that could take humans beyond the solar system.

Ignoring the major point that human tolerance of G forces is not the limiting factor on space travel, plenty of thought has been made on how to counteract G forces, not least by 60's scifi writers.

You can find more information than you ever wanted at Projectrho on this topic.

The general gist: for lowish accelerations like 2 G, you don't need to do anything special to the human body, just make sure you're lying either prone or on your back, and remaining disciplined about your breathing.

For higher Gs, like 5G+, you need to carefully manage the human body, putting it in a gel-like coccoon of similar density, and substituting air for a breathable liquid. Any differences in density can result in the denser parts of the body tending to 'settle' towards the back of the ship, and so must be avoided where possible.

Of course, such measures to counteract G forces can only ever be necessary with the use of nuclear or antimatter propellant. Chemical propellants do not burn for long enough to require such measures.

This is way beyond foreseeable economic possibilities, but the physics is sound:

Gravity is a surefire, scalable, elegant way to counteract G forces from acceleration.

A planet-sized spaceship with its own gravitational pull of 5 Gs could accelerate at 4 Gs, people living towards its tail would only experience the difference, one G.

(note that I'm talking about a ship roughly 5 times the mass of Earth, minus density differences)

The same is true for a ship with 100 Gs accelerating at 99 Gs.

Edit: moving the people through tunnels in the ship towards the front of it would allow for keeping the one G experience as propulsion slowly shifted to breaking.

G Force is a function of acceleration.
Gravity works on a mass to pull it toward another mass. Large masses have higher levels of gravitational attraction. The force of gravity on Jupiter and Saturn is stronger thatn that on earth. The moon less than on earth.

On earth gravity is a force that continues to pulls us down toward the center of the earth. The physical surface stops that acceleration. Our weight is the measure of that force acting on our mass.

Acceleration is a change in speed. When coasting (no acceleration nor deceleration forces) then there is no g-load (weightlessness in space).

Accelerating in a car, plane or spaceship causes G-Loads. Again, it is the acceleration that is causing the load. Banking an airplane in a 60 degree bank will cause g-loads on the body due to centripetal force. Looping and airplane will do the same. An inside look causes positive g-load while and outside loop causes negative g-load. Both are measured by effect on the body. When upright, positive g-loads causing blood to flow out of the head toward the feet and negative g-loads causing blood to flow from feet to head. human bodies tolerate positive g-loads better than negative. Lying down, like in many fighter jets help mitigate the impacts as more of the body is level.

So toleration of space travel is a combination of tolerating g-loads during accelerating and deceleration phases and weightlessness (absence of acceleration) periods which tend to affect muscles, bone densities, etc.