Let's set relativity aside for a moment. There's nothing in relativity preventing an object from traveling at .9c. So let's say the earth accelerated to .9c in October of year one of creation, and has been accelerating ever since, but somehow not surpassing .9c. When I was a kid in the early 70's, I was a bit into astronomy. I had a basic telescope, and I knew the names and locations of the common stars. Back then, the brightest star was Sirius A. Still is. Back then Sirius A was about 9 light years away. Still is. If earth were hurtling through the cosmos at .9c, Sirius could not be the same distance and brightness it was 45 years ago. It should be well in our rear view mirror by now. Depending on whether we were heading directly towards it, directly away, or somewhere in-between, it should be anywhere between 30 and 50 LY away, and considerably dimmer today. Yet it is not.
Most of the stars, including Sirius were known to the ancients. The ancient Egyptians knew about Orion, and provide us with plenty of drawings of the constellation from 4,000 years ago. It is roughly the same size and shape then as it is today. Which is clearly impossible on an earth traveling at .9c, or even .5c. The brightest star in Orion is Betelgeuse. It is 640 LY away today. Meaning that 4,000 years ago, it had to be 4240 LY away, and likely not visible to the naked eye.