From the perspective of someone on the spaceship, this is absolutely possible by the laws of physics. It's a common misunderstanding that the speed of light is like a highway speed limit that's enforced by the universe. In reality, it means that light always travels at the speed of light and that you can never observe an object traveling faster than that.

However, a key part of relativity is that the laws of physics are the same in every reference frame. If you're on a ship with sufficient fuel, you can keep accelerating forever and cover vast distances. You'll never reach a point where the universe prevents you from accelerating. If it were otherwise, then relativity wouldn't be true - because there would be special rules that apply to people traveling at a certain speed. That's the whole point of relativity is there can't be such laws because there isn't a preferred reference frame in the universe!

However, the more you accelerate away from the earth the longer time will have passed on earth if you turn around and come back.

Here's a calculator you can play with: https://spacetravel.simhub.online

As an example, if you could accelerate at 9.8 m/s (same as gravity - so you could walk around the 'back' of the ship as if in earth gravity), then you could travel 50 light years in 7.7 'ship years'. However, if you turned around and went back to earth 102 years would have passed there, even though you would only be ~15 years older.