G force occurs ONLY during acceleration and deceleration. If you were to travel at a CONSTANT, non-accelerating speed (ANY speed) then the would be NO G-forces. For example, A jet fighter in a tight turn can do 9-11 G's at 200 MPH. But the International Space Station, traveling at a constant 17.500 MPH, has NO G's, and objects are weightless
SO . . . G-forces can be controlled by how fast you accelerate towards warp speed, and how slow you decelerate from warp speed. You COULD accelerate at ONE G, but it would take you MUCH MUCH longer to get up to warp speed.
a sudden JUMP to warp speed MIGHT mean a very high G-force, a force which Star Trek deals with by inventing "Inertial Dampers" which override the inertia that causes the G-force during acceleration or deceleration.
But consider this: The whole idea of Warp Speed is NOT to move faster, but to move a shorter distance. A "Warp Drive" actually "warps space" in front of it, such that the path to the destination is SHORTER than it is in unwarped space. With "warp drive" NOTHING actually even comes close to the speed of light! Space is "warped", you travel across the warp at very much sub-light speed, then release the warp behind you.
Consider it this way: If you could "warp space" enough that the surface of Mars was just across the street, you could WALK TO MARS in 10 minutes, then release the warp. It would APPEAR that you traveled 20 million miles in 10 minutes, but you NEVER exceeded about 4 MPH, with a ridiculously low G-force of, like, 0.003 Gs
Warp drive is NOT about speed!