The existing proposals for superfluid spin transport have been based on easy-plane magnets where the U(1) spin-rotational symmetry is spontaneously broken in equilibrium, and this has been limiting material choices for realizing superfluid spin transport to restricted class of magnets. In this work, we lift this limitation by showing that superfluid spin transport can also be realized based on easy-axis magnets, where the U(1) spin-rotational symmetry is intact in equilibrium but can be broken in non-equilibrium. Specifically, we find the condition to engender a non-equilibrium easy-cone state by applying a spin torque to easy-axis magnets, which dynamically induces the spontaneous breaking of the U(1) spin-rotational symmetry and thereby can support superfluid spin transport. By exploiting this dynamic easy-cone state, we show theoretically that superfluid spin transport can be achieved in easy-axis magnets under suitable conditions and confirmed the prediction by micromagnetic simulations. We envision that our work broadens material library for realizing superfluid spin transport, showing the potential utility of dynamic states of magnets as venue to look for spin-transport phenomena that do not occur in static magnetic backgrounds.