  We report an experimental study of the emergence of non-trivial topological
winding and long-range order across the paramagnetic to skyrmion lattice
transition in the transition metal helimagnet MnSi. Combining measurements of
the susceptibility with small angle neutron scattering, neutron resonance spin
echo spectroscopy and all-electrical microwave spectroscopy, we find evidence
of skyrmion textures in the paramagnetic state exceeding $10^3$\AA with
lifetimes above several 10$^{-9}$s. Our experimental findings establish that
the paramagnetic to skyrmion lattice transition in MnSi is well-described by
the Landau soft-mode mechanism of weak crystallization, originally proposed in
the context of the liquid to crystal transition. As a key aspect of this
theoretical model, the modulation-vectors of periodic small amplitude
components of the magnetization form triangles that add to zero. In excellent
agreement with our experimental findings, these triangles of the
modulation-vectors entail the presence of the non-trivial topological winding
of skyrmions already in the paramagnetic state of MnSi when approaching the
skyrmion lattice transition.
