No, because the speed of light is constant for all observers. From our frame of reference on earth, light from distant receding galaxies is always moving towards us at exactly the speed of light, c. Those galaxies also observe the light moving away from them at exactly c.
That seems contradictory and unintuitive, that two observers moving away from each other both measure light moving c relative to themselves, but that’s reality.
It’s another measurement that changes: if c is always constant, then it must be the passage of time and the distance travelled that we observe differently.