  We present the first exploratory lattice quantum chromodynamics (QCD)
calculation of the polarized gluon Ioffe-time pseudo-distribution in the
nucleon. The Ioffe-time pseudo-distribution provides a frame-independent and
gauge-invariant framework to determine the gluon helicity in the nucleon from
first principles. We employ a high-statistics computation using a $32^3\times
64$ lattice ensemble characterized by a $358$ MeV pion mass and a $0.094$ fm
lattice spacing. We establish the pseudo-distribution approach as a feasible
method to address the proton spin puzzle with successive improvements in
statistical and systematic uncertainties anticipated in the future. Within the
statistical precision of our data, we find a good comparison between the
lattice determined polarized gluon Ioffe-time distribution and the
corresponding expectations from the state-of-the-art global analyses. We find a
hint for a nonzero gluon spin contribution to the proton spin from the
model-independent extraction of the gluon helicity pseudo-distribution over a
range of Ioffe-time, $\nu\lesssim 9$.
