by the Pauli matrices. This singular structure has been attributed to the approximation used to avoid the sign problem in the Monte Carlo simulation. Indeed a clear departure from the Pauli-matrix structure has been observed in Ref. [@Nishimura:2019qal], where the sign problem was treated correctly by the complex Langevin method for a simpler bosonic Lorentzian model. Based on this observation, it has been conjectured that a smooth (3+1)-dimensional expanding space-time should emerge dynamically from the Lorentzian type IIB matrix model in the large-$N$ limit. Our results for the classical solutions support this conjecture. Another issue we would like to address in this paper concerns how the Standard Model particles emerge from the type IIB matrix model at low energy. In fact, Refs. [@Chatzistavrakidis:2011gs; @Steinacker:2014fja; @Aoki:2014cya] discussed matrix configurations representing intersecting D-branes that can accommodate Standard Model fermions although it was not clear whether such configurations can be realized as classical solutions. Here we find that a slight extension of the simple direct-product structure, which we refer to as the “quasi” direct-product structure above, naturally realizes classical solutions with a block-diagonal structure in the extra dimensions, which corresponds to intersecting D-branes. By choosing the dimensionality of the intersecting D-branes appropriately, we 