We develop a new dynamical model for high energy heavy-ion collisions in the beam energy region of the highest net-baryon densities on the basis of non-equilibrium microscopic transport model JAM and macroscopic 3+1D hydrodynamics by utilizing a dynamical initialization method. In this model,dynamical fluidization of a system is controlled by the source terms of the hydrodynamic fields. In addition, time dependent core-corona separation of hot regions is implemented. We show that our new model describes multiplicities and mean transverse mass in heavy-ion collisions within a beam energy region of $3<sqrt{s_{NN}}<30$ GeV. Good agreement of the beam energy dependence of the $K^+/pi^+$ ratio is obtained, which is explained by the fact that a part of the system is not thermalized in our core-corona approach.