What does the speed of light being the fastest possible speed really mean? It's not as simple as it first seems. The speed limit only applies to the speed of objects seen to be passing each other.
For example, consider a very distant galaxy. It may be moving away from us very fast because of the expansion of the universe; its speed may be a significant fraction of that of light. The faster a galaxy is moving away from us, the more its light is red-shifted. Eventually this galaxy will be moving away from us faster than light, but we will never see this, as its light will be red-shifted into darkness. We will see the galaxy disappear.
Another example is a spaceship travelling close to the speed of light. It can, from the passenger's point of view, travel faster than light because of time dilation and distance contraction. Accelerating at 1 g it would be possible to get to the centre of the galaxy in decades, even though its about 30,000 light years away. However, nothing is seen to be passing the ship faster than light because distances will seem shortened in the direction of travel. Nothing is seen to be passing the ship faster than light from outside the ship, because from that viewpoint the ship never travels faster than light!
Light speed isn't the barrier it seems to be at first - it's just the limit at which things can be seen to travel.