This numerical study aims to investigate the influence of I and T-shaped empty channels’ geometry on the filling time of resin in a rectangular porous enclosed mold, mimicking the main operating principle of a liquid resin infusion (LRI) process. Geometrical optimization was conducted with the constructal design (CD) and exhaustive search (ES) methods. The problem was subjected to two constraints (areas of porous mold and empty channels). In addition, the I and T-shaped channels were subjected to one and three degrees of freedom (DOF), respectively. Conservation equations of mass and momentum for modeling of resin/air mixture flow were numerically solved with the finite volume method (FVM). Interaction between the phases was considered with the volume of fluid method (VOF), and the effect of porous medium resistance in the resin flow was calculated with Darcy’s law. For the studied conditions, the best T-shaped configuration resulted in a filling time nearly three times lower than that for optimal I-shaped geometry, showing that the complexity of the channels benefited the performance. Moreover, the best T-shaped configurations were achieved for long single and bifurcated branches, except for configurations with skinny channels, which saw the generation of permanent voids.