  We report on the first observation of the diffuse cosmic neutrino flux with
the Baikal-GVD neutrino telescope. Using cascade-like events collected by
Baikal-GVD in 2018--2021, a significant excess of events over the expected
atmospheric background is observed. This excess is consistent with the
high-energy diffuse cosmic neutrino flux observed by IceCube. The null cosmic
flux assumption is rejected with a significance of 3.05$\sigma$. Assuming a
single power law model of the astrophysical neutrino flux with identical
contribution from each neutrino flavor, the following best-fit parameter values
are found: the spectral index $\gamma_{astro}$ = $2.58^{+0.27}_{-0.33}$ and the
flux normalization $\phi_{astro}$ = 3.04$^{+1.52}_{-1.21}$ per one flavor at
100 TeV.
