The observation that is most likely related to the Doppler effect and led to the discovery that the Universe is expanding is:
When observed from Earth, light spectra from stars in other galaxies have redshifts.
This observation indicates that many galaxies are moving away from us, which supports the theory that the Universe is expanding. The redshift of light from distant galaxies was a key piece of evidence that helped scientists like Edwin Hubble conclude that the Universe itself is expanding.