universe - Can there be a 2nd possibility deduced from the fact that galaxies are moving away from us?

Galaxies are moving away from us in every direction.

If it were like your race, galaxies at our same distance from the central point will be slowly approximating. That is, we will note that galaxies nearer to the center than us will move away from us (since they are faster), galaxies in the opposite side of the sky will move away from us (since they are slower), and galaxies in the plane that lies between these two point will be slowly approximating to us (since we converge with them to the same point at the same speed).

So the answer is no, that is not a possibility.