How does the big bang theory explain the observed doppler effect from other galaxies?

Well if the big bang happened, that means the universe is expanding. If the universe is expanding, everything is moving away from everything else from the Epicenter of the Big Bang. If an object is moving away from us, its light will undergo a doppler shift to the red end of the spectrum. If an object moved towards us, light would be blue-shifted. Since most objects we see in the sky are red-shifted and thus moving away from us, the Big Bang Theory explains why everything is moving away from us.