Pressure-induced nearly perfect rectangular lattice and superconductivity in an organic molecular crystal (DMET-TTF)$_2$AuBr$_2

External pressure and associated changes in lattice structures are key to realizing exotic quantum phases such as high-$T_{\rm c}$ superconductivity. While applying external pressure is a standard method to induce novel lattice structures, its impact on organic molecular crystals has been less explored. Here we report a unique structural phase transition in (DMET-TTF)$_2$AuBr$_2$ under pressure. By combining advanced high-pressure techniques and $ab$ $initio$ calculations, we elucidate that (DMET-TTF)$_2$AuBr$_2$ undergoes a transition from a quasi-one-dimensional lattice to a nearly perfect rectangular lattice at 0.9 GPa. This transition leads to the realization of an antiferromagnetic Mott insulator with $T_{\rm N}=66$ K, the highest $T_{\rm N}$ in low-dimensional molecular crystal solids to date. Upon increasing the pressure, the antiferromagnetic ordering is suppressed, and a superconducting phase with $T_{\rm c}=4.8$ K emerges around 6 GPa. Our study reveals the significant impact of external pressure on lattice structures of organic molecular crystals and highlights the intricate relationship between geometrical frustration and superconductivity. Our findings also pave the way for realizing functional organic molecular crystals through changes in lattice structures by pressure.