ordinary classical dynamics, in which one solves a differential equation with some initial conditions. This is because the notion of time does not exist from the outset in this model, and it should emerge dynamically from the matrix degrees of freedom. Here we propose a method based on the gradient decent method, which enables us to generate infinitely many classical solutions starting from random matrix configurations. In particular, we assume a “quasi” direct-product structure for the (3+1) dimensions and the extra six dimensions, which is the most general structure compatible with the (3+1)-dimensional Lorentz symmetry [@Nishimura:2013moa]. Our ultimate goal is to determine the solution that describes our real world by identifying a specific solution that appears from the dominant configurations obtained by numerical simulations. We consider that some if not all of the qualitative features of such a solution should be captured by the solutions generated by our method. In typical solutions, we find that the (3+1)-dimensional space-time exhibits an expanding behavior with a smooth structure. This is in sharp contrast to the situation with the previous Monte Carlo studies of the Lorentzian type IIB matrix model [@Aoki:2019tby], where it was found that the 3-dimensional expanding space is described essentially 