Colloidal open crystals are attractive materials, especially for their photonic applications. Self-assembly appeals as a bottom-up route for structure fabrication, but self-assembly of colloidal open crystals has proven to be elusive for their mechanical instability due to being low-coordinated. For such a bottom-up route to yield a desired colloidal open crystal, the target structure is required to be thermodynamically favored for designer building blocks and also kinetically accessible via self-assembly pathways in preference to metastable structures. Additionally, the selection of a particular polymorph poses a challenge for certain much sought-after colloidal open crystals for their applications as photonic crystals. Here, we devise hierarchical self-assembly pathways, which, starting from designer triblock patchy particles, yield in a cascade of well-separated associations first tetrahedral clusters and then tetrastack crystals. The designed pathways avoid trapping into an amorphous phase. Our analysis reveals how such a two-stage self-assembly pathway via tetrahedral clusters promotes crystallization by suppressing five- and seven-membered rings that hinder the emergence of the ordered structure. We also find that slow annealing promotes a bias toward the cubic polymorph relative to the hexagonal counterpart. Finally, we calculate the photonic band structures, showing that the cubic polymorph exhibits a complete photonic band gap for the dielectric filling fraction directly realizable from the designer triblock patchy particles. Unexpectedly, we find that the hexagonal polymorph also supports a complete photonic band gap, albeit only for an increased filling fraction, which can be realized via postassembly processing.