Let me put this as blunt as I can with my limited knowledge in physics.
When something goes fast, it's time is slower relative to itself. When something goes to the speed of light, time stops relative to it, but it keeps going, and very quickly relative to every other thing. To get to the speed of light requires infinite energy, and if you go to light-speed, everything else seems to stop. Now, technically, space-time is relative; that's the simplest way to put the Theory of Relativity. However, one does not GO BACK IN TIME RELATIVE TO THE UNIVERSE, simply due to going fast enough. Even IF it does not take infinite energy to make matter go to light-speed; that part being wrong for the sake of argument, It seems VERY unlikely that it would send something back in time. Cherenkov Radiation goes faster than light, and that doesn't send it back in time. It's observable within current space time.
Now, that's because it's energy. Matter is slower. I'm not sure how it works, but the best way of thinking of it is, and I may still be mistaken, that the more to a sub-atomic particle, or the more there is interacting with it the slower it can go. I believe this is called drag, though that's probably a crude way of defining this. Photons, or light, go the speed they do because photons are limited to the speed of light. Some sub-atomic particles go faster than light, because they're much lighter, and aren't slowed down easily by other particles.
If a star went faster than light, it might appear far, far more luminous than it is in its own time. That's the problem, though, because it would burn out in an instant in our time. Some bored telescope enthusiast might notice it and give it a name that's three letters followed by a dozen digits, but the next moment he looked, he'd be all like "hey where did it go why did it disappear what is this i dont even". Simply put said stars would not be "alive" at the speeds you're implying. For them to do such would require technology that not even humans are capable of yet- and remember, we're talking about something that is not even as autonomous as an amoeba.
Now, I know the next logical arguments against what I said are that God can do whatever and all that- well, think of how silly it is for him to send stars fifty-thousand-something billion years into the past, then make Earth and the Sol system. Well, assuming he isn't bothered by time, why not just make all the stars and junk at day-one of the universe, and let it go on naturally, then make everything else at the logical intervals when needed? I mean, you're talking about someone who isn't limited to anything and can to whatever he needs or wants. He COULD send the stars that are so insanely numerous that there's not a word for how many of them there are back in time; it's not hard for him at all. However, if I've learned anything about God, he's a live-and-let-live person most of the time, is very old, and like most old people, is very patient. If I were very patient, very old, very bored, and there was like nothing at all to do, I wouldn't have any problem creating countless stars and natural wonders over a course of trillions of years, and then if I felt like it, create life on some vaguely spherical rock in a random planetary system, then make some sentient bipedal critters there because I didn't have anyone to talk to.
You see, the Universe is sort of like an art film that nerds are fans of and try to make sense out of. Like
2001: A Space Odyssey, except it has a coherent story that makes sense, and there aren't gigantic black space mattresses stood on their sides to make monkeys kill things with bones. Mind you, it's still boring most of the time to humans. The thing is, though, when someone is infinitely powerful and like so old that a million years feels like a day, it makes sense that the universe's age would be measured in trillions of years instead of thousands.
And one last thing; the guy who said the universe is six-thousand years old said that about a thousand years ago. So if you're going to go in that direction, you should be saying it's
seven thousand years, not six.
P.S.: Also The Blue Danube doesn't play in space. I think Buzz Aldrin would have told us if that were the case. After all, he went to the moon and saw a monolith on Phobos.He knows what he's talking about.