  We study the existence of skyrmions in the presence of all the electroweak
degrees of freedom, including a dynamical Higgs boson, with the electroweak
symmetry being non-linearly realized in the scalar sector. For this, we use the
formulation of the Higgs Effective Field Theory (HEFT). In contrast with the
linear realization, a well-defined winding number exists in HEFT for all scalar
field configurations. We classify the effective operators that can potentially
stabilize the skyrmions and numerically find the region in parameter spaces
that support them. We do so by minimizing the static energy functional using
neural networks. This method allows us to obtain the minimal-energy path
connecting the vacuum to the skyrmion configuration and calculate its mass and
radius. Since skyrmions are not expected to be produced at colliders, we
explore the experimental and theoretical bounds on the operators that generate
them. Finally, we briefly consider the possibility of skyrmions being dark
matter candidates.
