Multiscale self-assembly is ubiquitous in nature but its deliberate use to synthesize multifunctional three-dimensional materials remains rare, partly due to the notoriously difficult problem of controlling topology from atomic to macroscopic scales to obtain intended material properties. Here, we propose a simple, modular, noncolloidal methodology that is based on exploiting universality in stochastic growth dynamics and driving the growth process under far-from-equilibrium conditions toward a preplanned structure. As proof of principle, we demonstrate a confined-but connected solid structure, comprising an anisotropic random network of silicon quantum-dots that hierarchically self-assembles from the atomic to the microscopic scales. First, quantum-dots form to subsequently interconnect without inflating their diameters to form a random network, and this network then grows in a preferential direction to form undulated and branching nanowire-like structures. This specific topology simultaneously achieves two scale-dependent features, which were previously thought to be mutually exclusive: good electrical conduction on the microscale and a bandgap tunable over a range of energies on the nanoscale.