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Supernovae (SNe) dominate the energy and momentum budget of stellar feedback, but the efficiency with which they couple to the interstellar medium (ISM) depends strongly on how effectively early, pre-SN feedback clears dense gas from star-forming regions. There are observational constraints on the magnitudes and timescales of early stellar feedback in low ISM pressure environments, yet no such constraints exist for more cosmologically typical high ISM pressure environments. In this paper, we determine the mechanisms dominating the expansion of HII regions as a function of size-scale and evolutionary time within the high-pressure ($P/k_\rm{B}$~$10^{7-8}$K cm$^{-3}$) environment in the inner 100pc of the Milky Way. We calculate the thermal pressure from the warm ionised ($P_\rm{HII}$; 10$^{4}$K) gas, direct radiation pressure ($P_\rm{dir}$), and dust processed radiation pressure ($P_\rm{IR}$). We find that (1) $P_\rm{dir}$ dominates the expansion on small scales and at early times (0.01-0.1pc; $<$0.1Myr); (2) the expansion is driven by $P_\rm{HII}$ on large scales at later evolutionary stages ($>0.1$pc; $>1$Myr); (3) during the first ~1Myr of growth, but not thereafter, either $P_{\rm IR}$ or stellar wind pressure likely make a comparable contribution. Despite the high confining pressure of the environment, natal star-forming gas is efficiently cleared to radii of several pc within ~2Myr, i.e. before the first SNe explode. This `pre-processing' means that subsequent SNe will explode into low density gas, so their energy and momentum will efficiently couple to the ISM. We find the HII regions expand to a radius of 3pc, at which point they have internal pressures equal with the surrounding external pressure. A comparison with HII regions in lower pressure environments shows that the maximum size of all HII regions is set by pressure equilibrium with the ambient ISM.