Don't be fooled by these glib answers, Ori. This is just another absurdity created by abandoning all standards.
If a ship is constantly accelerating at 1g then it will reach the speed of light in a little less than a year. For it to just keep on accelerating after that, it would have to exceed the speed of light, which is supposedly impossible.
One "gimmick" is to say it won't "look" that way to people on earth. No matter how fast it is going, we will never "see" it to be faster than the speed of light. "Appearance" becomes reality, for those with no sense of reality.
The same absurdity applies to the ship. It too will never reach the speed of light from it's perspective. For this reason it could will never "see" itself as exceeding the speed of light. It can go 13.7 billions light years in just 23 years, or so it says:
After experiencing the passage of twenty-three years, the astronauts would actually pass the edge of the universe currently observable from Earth, but 13.7 billion years would have elapsed in the reference frame of a long-dead Earth.
When you're constantly changing standards for MEASURING space and time, then there is no standard whatsoever. There are no limits whatsoever.
So if we say we "see" light from 13.7 billions years ago, that could only be 23 years in "reality." Which means we could never know how far away it "really" is (how far it really travelled), because whatever speed it's travelling at (how much distance it has covered in how much time) has NOTHING to do with how we measure it. We will measure it as always being the same (186,000 miles per second), regardless.
Note also that using the word "see" here means nothing. It is not something we "see" with our eyes. It is a mental conclusion strictly deduced mathematically from presupposed premises.