  The type IIB matrix model is a promising candidate for a nonperturbative
formulation of superstring theory. As such, it is expected to explain the
origin of space--time and matter at the same time. This has been partially
demonstrated by the previous Monte Carlo studies on the Lorentzian version of
the model, which suggested the emergence of (3+1)-dimensional expanding
space--time. Here we investigate the same model by solving numerically the
classical equation of motion, which is expected to be valid at late times since
the action becomes large due to the expansion of space. Many solutions are
obtained by the gradient descent method starting from random matrix
configurations, assuming a quasi-direct-product structure for the
(3+1)-dimensions and the extra 6 dimensions. We find that these solutions
generally admit the emergence of expanding space--time and a block-diagonal
structure in the extra dimensions, the latter being important for the emergence
of intersecting D-branes. For solutions corresponding to D-branes with
appropriate dimensionality, the Dirac operator is shown to acquire a zero mode
in the limit of infinite matrix size.
