  The moir\'e engineering of two-dimensional magnets opens unprecedented
opportunities to design novel magnetic states with promises for spintronic
device applications. The possibility of stabilizing skyrmions in these
materials without chiral spin-orbit couplings or dipolar interactions is yet to
be explored. Here, we investigate the formation and control of ground state
topological spin textures (TSTs) in moir\'e CrI3 using stochastic
Landau-Lifshitz-Gilbert simulations. We unveil the emergence of interlayer
vortex and antivortex Heisenberg exchange fields, stabilizing spontaneous and
field-assisted ground state TSTs with various topologies. The developed study
accounts for the full bilayer spin dynamics, thermal fluctuations, and
intrinsic spin-orbit couplings. By examining the effect of the Kitaev
interaction and the next nearest-neighbor Dzyaloshinskii-Moriya interaction, we
propose the latter as the unique spin-orbit coupling mechanism compatible with
experiments on monolayer and twisted CrI3. Our findings contribute to the
current knowledge about moir\'e skyrmionics and uncover the nature of
spin-orbit coupling in CrI3.
