Abstract We present in this Letter the first global comparison between traditional line-tied steady-state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. To approximate surface magnetic field distributions and magnitudes around solar minimum, we use the Lockheed Evolving Surface-Flux Assimilation Model to obtain input maps that incorporate flux emergence and surface flows over a full solar rotation, including differential rotation and meridional flows. Each time step evolves the previous state of the plasma with a new magnetic field input boundary condition, mimicking photospheric driving on the Sun. We find that this method produces a qualitatively different corona compared to steady-state models. The magnetic energy levels are higher in the time-dependent model, and coronal holes evolve more along the following edge than they do in steady-state models. Coronal changes, as illustrated with forward-modeled emission maps, evolve on longer timescales with time-dependent driving. We discuss implications for active and quiet Sun scenarios, solar wind formation, and widely used steady-state assumptions like potential field source surface calculations.