While the Landauer viewpoint constitutes a modern basis to understand nanoscale electronic transport and to realize first-principles implementations of the nonequilibrium Green's function (NEGF) formalism, seeking an alternative picture can be beneficial for the fundamental understanding and practical calculations of quantum transport processes. Herein, introducing a micro-canonical picture that maps the finite-bias quantum transport process to a drain-to-source or multi-electrode optical excitation, the multi-space constrained-search density functional theory (MS-DFT) formalism for first-principles electronic structure and quantum transport calculations is developed. Performing MS-DFT calculations for the benzenedithiolate single-molecule junction, it is shown that MS-DFT and standard DFT-NEGF calculations produce practically equivalent electronic and transmission data. Importantly, the variational convergence of "nonequilibrium total energy" within MS-DFT is demonstrated, which should have significant implications for in operando studies of nanoscale devices. Establishing a viable alternative to the Landauer viewpoint, the developed formalism should provide valuable atomistic information in the development of next-generation nanodevices.