  We propose a protocol for realizing the stripe phase in two spin models on a
two-dimensional square lattice, which can be implemented with strongly magnetic
atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into
Zeeman sublevels of the ground state manifold. The protocol is tested with
cluster-mean-field time-dependent variational ans\"atze, validated by
comparison with exact results for small systems, which enable us to simulate
the dynamics of systems with up to 64 sites during the state-preparation
protocol. This allows, in particular, to estimate the time required for
preparation of the stripe phase with high fidelity under real experimental
conditions.
