The solar magnetic field expands outward from the Sun with the solar wind and fills the heliosphere. Understanding the structure, dynamics, and connectivity of this field underlies many unanswered questions in solar and heliospheric physics. The field is most readily measured in the photosphere, so models must extrapolate this field out into the solar wind. We describe a continuously updated, time-evolving magnetohydrodynamic (MHD) model of the solar corona and inner heliosphere, extending from the upper chromosphere to 1 AU, run for a month of evolution during the time leading up to the April 8, 2024 total solar eclipse. The model assimilates magnetograms from the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory into a surface flux transport (SFT) model, which is used to create full-Sun boundary conditions for the MHD model. The time-evolving model is highly dynamic, with many small-scale eruptions, and at time exhibits complex magnetic field structures. We compare the results of the dynamic model with steady-state MHD and PFSS models created with the same boundary data, including differences in the magnetic connectivity predicted by the models at L1 and other spacecraft locations.