Understanding dynamics of pattern formation, following a symmetry breaking quantum phase transition is an area of active interest. Spontaneous spin domain is formed in sodium Bose-Einstein condensates that are quenched, i.e. rapidly tuned, through a quantum phase transition from polar to antiferromagnetic phases. A microwave ``dressing'' field globally shifts the energy of the m_F= 0 level below the average of the m_F= ±1 energy levels, inducing a dynamical instability . We use local spin measurements to quantify the spatial ordering kinetics in the vicinity of the phase transition. For an elongated BEC, the instability nucleates small antiferromagnetic domains near the center of the polar condensate that grow in time along one spatial dimension. After a rapid nucleation and coarsening phase, the system exhibits long timescale non-equilibrium dynamics without relaxing to a uniform antiferromagnetic phase.