  We present the first measurement of nuclear recoils from solar $^8$B
neutrinos via coherent elastic neutrino-nucleus scattering with the XENONnT
dark matter experiment. The central detector of XENONnT is a low-background,
two-phase time projection chamber with a 5.9\,t sensitive liquid xenon target.
A blind analysis with an exposure of 3.51\,t$\times$y resulted in 37 observed
events above 0.5\,keV, with ($26.4^{+1.4}_{-1.3}$) events expected from
backgrounds. The background-only hypothesis is rejected with a statistical
significance of 2.73\,$\sigma$. The measured $^8$B solar neutrino flux of
$(4.7_{-2.3}^{+3.6})\times 10^6\,\mathrm{cm}^{-2}\mathrm{s}^{-1}$ is consistent
with results from dedicated solar neutrino experiments. The measured neutrino
flux-weighted CE$\nu$NS cross-section on Xe of
$(1.1^{+0.8}_{-0.5})\times10^{-39}\,\mathrm{cm}^2$ is consistent with the
Standard Model prediction. This is the first direct measurement of nuclear
recoils from solar neutrinos with a dark matter detector.
