  One of the great challenges of QCD is to determine the partonic structure of
the nucleon from first principles. In this work, we provide such a
determination of the flavor non-singlet ($u-d$) unpolarized parton distribution
function (PDF), utilizing the non-perturbative formulation of QCD on the
lattice. We apply Radyushkin's pseudo-distribution approach to lattice results
obtained using simulations with the light quark mass fixed to its physical
value; this is the first ever attempt for this approach directly at the
physical point. The extracted coordinate-space matrix elements are used to find
the relevant physical Ioffe time distributions from a matching procedure. The
full Bjorken-$x$ dependence of PDFs is resolved using several reconstruction
methods to tackle the ill-conditioned inverse problem encountered when using
discrete lattice data. We consider both the valence distribution $q_v$ and the
combination with antiquarks $q_v+2\bar{q}$, related to, respectively, the real
and imaginary part of extracted matrix elements. Good agreement is found with
PDFs from global fits already within statistical uncertainties and it is
further improved by quantifying several systematic effects. The results
presented here are the first ever \emph{ab initio} determinations of PDFs fully
consistent with global fits in the whole $x$-range. Thus, they pave the way to
investigating a wider class of partonic distributions, such as e.g.\ singlet
PDFs and generalized parton distributions. Therefore, essential and yet missing
first-principle insights can be achieved, complementing the rich experimental
programs dedicated to the structure of the nucleon.
