Not unless we were directly in the center of it, in which case everything would seem to move away from us. But even then, if I’m not mistaken, physicists and astronomers have also proven that other objects are also moving away from one another too.
We can tell how something is moving based on the shift of its light, like the Doppler effect. The further something is the more its light is shifted, which was how we came to know this phenomenon in general of increasing size of space between all things.