If I understand the basics of the big bang correctly it starts with a very small dense point. At the moment of the big bang, less then microseconds after, the universe is already the size of our solar system. That would mean the particles traveled faster than light. How can these particles travel faster than light? My understanding is nothing should be able to faster.
I am just hoping on finding a glitch in the system so we will have warp speed soon to visit all those distant planets.
It is a misunderstanding that everything was traveling faster then light at the big bang. GR and SR states that nothing, no matter and no particles can travel, no information can travel faster then light when measured locally in vacuum.
Now at the big bang, as you mention, the size of the universe was a very small dense point, and one microsecond later, it was as big as the solar system. That is because space itself was expanding faster then light.
Nothing was traveling faster then light.
It was the space between particles of matter (between all elementary particles) that was expanding faster then light. There is no contradiction with SR nor GR.
It is a common misconception that particles flew away faster than light.
A similar question that how can galaxies far enough recede at twice the speed of light from us.
If you have seen the balloon inflation model then you will understand that the galaxies are not traveling faster than the light, but the space between them is expanding at a rate that makes them appear as if they are moving faster than light.
Similarly the particles in start of universe didn't move faster than light rather the space between particles expanded so fast that they appeared to recede away from each other faster than the speed of light.
