  We report on the first search for nuclear recoils from dark matter in the
form of weakly interacting massive particles (WIMPs) with the XENONnT
experiment which is based on a two-phase time projection chamber with a
sensitive liquid xenon mass of $5.9$ t. During the approximately 1.1 tonne-year
exposure used for this search, the intrinsic $^{85}$Kr and $^{222}$Rn
concentrations in the liquid target were reduced to unprecedentedly low levels,
giving an electronic recoil background rate of
$(15.8\pm1.3)~\mathrm{events}/(\mathrm{t\cdot y \cdot keV})$ in the region of
interest. A blind analysis of nuclear recoil events with energies between $3.3$
keV and $60.5$ keV finds no significant excess. This leads to a minimum upper
limit on the spin-independent WIMP-nucleon cross section of $2.58\times
10^{-47}~\mathrm{cm}^2$ for a WIMP mass of $28~\mathrm{GeV}/c^2$ at $90\%$
confidence level. Limits for spin-dependent interactions are also provided.
Both the limit and the sensitivity for the full range of WIMP masses analyzed
here improve on previous results obtained with the XENON1T experiment for the
same exposure.
