A theoretical model has been developed to elucidate the thermal initiation laser ignition process of solid fuel. This model comprehensively explores both the heating process of solid fuel and the mixing process of gas-phase pyrolysis gases with crossflow conditions. A two-dimensional transient numerical model has been established and validated through experimental investigations across a spectrum of crossflow fluxes (ranging from 20 to 150 kg/m2/s) and pressures (ranging from 0.15 to 1.83 MPa). The study involves a quantitative analysis of the influence of key macroscopic parameters, including laser energy levels, combustion pressure, and flow rates, on essential mixing characteristics. The solid fuel heating process is segmented into two distinct phases: a preheating phase and a pyrolysis phase, with the latter exhibiting considerably higher heating rates. Notably, a direct linear relationship is observed between the laser energy levels and the rate of heating. It reveals that the dynamics of pyrolysis product mixing are primarily determined by the solid fuel pyrolysis rate and the prevailing crossflow conditions. The dimensionless penetration depth, which measures the extent of pyrolysis product mixing with crossflow, demonstrates an exponential positive correlation with pyrolysis rates and oxidizer flow rates while displaying a negative correlation with combustion pressure. This analysis includes the quantitative determination of proportionality constants and power exponents within the correlations. Finally, the study delves into the intricate interplay between crossflow conditions and the criteria for laser ignition, specifically ignition temperature and the flammable lower limit.