  We show that the full Horndeski theory with both curvature and torsion can
support nonsingular, stable and subluminal cosmological solutions at all times.
Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is
avoided. In particular, it is essential to include the nonminimal derivative
couplings of the $\mathcal{L}_{5}$ part of the Horndeski action
($G^{\mu\nu}\,\nabla_\mu \nabla_\nu \phi,$ and $(\nabla^2 \phi)^3$). Without
the latter a No-Go already impedes the eternal subluminality of nonsingular,
stable cosmologies.
