In the late stages of the HIV-1 life cycle, membrane localization and self-assembly of Gag polyproteins induce membrane deformation and budding. Release of the virion requires direct interaction between immature Gag lattice and upstream ESCRT machinery at the viral budding site, followed by assembly of downstream ESCRT-III factors, culminating in membrane scission. However, molecular details of upstream ESCRT assembly dynamics at the viral budding site remain unclear. In this work, using coarse-grained (CG) molecular dynamics (MD) simulations, we investigated the interactions between Gag, ESCRT-I, ESCRT-II, and membrane to delineate the dynamical mechanisms by which upstream ESCRTs assemble templated by late-stage immature Gag lattice. We first systematically derived "bottom-up" CG molecular models and interactions of upstream ESCRT proteins from experimental structural data and extensive all-atom MD simulations. Using these molecular models, we performed CG MD simulations of ESCRT-I oligomerization and ESCRT-I/II supercomplex formation at the neck of the budding virion. Our simulations demonstrate that ESCRT-I can effectively oligomerize to higher-order complexes templated by the immature Gag lattice both in the absence of ESCRT-II and when multiple copies of ESCRT-II are localized at the bud neck. The ESCRT-I/II supercomplexes formed in our simulations exhibit predominantly columnar structures, which has important implications for the nucleation pathway of downstream ESCRT-III polymers. Importantly, ESCRT-I/II supercomplexes bound to Gag initiate membrane neck constriction by pulling the inner edge of the bud neck closer to the ESCRT-I headpiece ring. Our findings serve to elucidate a network of interactions between upstream ESCRT machinery, immature Gag lattice, and membrane neck that regulate protein assembly dynamics at the HIV-1 budding site.