Abstract We employed the dinuclear system (DNS) model combined with statistical model to calculate the evaporation residue cross sections for the reaction systems $^{48}$Ca + $^{243}$Am, $^{48}$Ca + $^{248}$Cm, and $^{48}$Ca + $^{249}$Bk. The theoretical results successfully reproduced the experimental trends in the 3$n$ and 4$n$ evaporation channels of these reaction systems. In order to synthesize the new element $Z = 119$, we predicted the evaporation residue cross sections for three reaction systems ($^{54}$Cr + $^{243}$Am, $^{51}$V + $^{248}$Cm, and $^{50}$Ti + $^{249}$Bk) to select the most promising projectile-target combinations. We also noted that the maximum cross sections predicted by our model and other methods appear to be below the detection limits of current experimental facilities, given the projectile-target combinations feasible under current experimental conditions. Therefore, synthesizing superheavy nuclei with $Z = 119$ will require improvements in beam intensity, detection techniques, and effective separation methods.