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Early dark energy (EDE), whose cosmological role is localized in time around the epoch of matter-radiation equality in order to resolve the Hubble tension, introduces a new coincidence problem: why should the EDE dynamics occur near equality if EDE is decoupled from both matter and radiation? The resolution of this problem may lie in an {\it early dark sector} (EDS), wherein the dark matter mass is dependent on the EDE scalar field. Concretely, we consider a Planck-suppressed coupling of EDE to dark matter, as would naturally arise from breaking of the global $U(1)$ shift symmetry of the former by quantum gravity effects. With a sufficiently flat potential, the rise to dominance of dark matter at matter-radiation equality itself triggers the rolling and subsequent decay of the EDE. We show that this {\it trigger} EDS (tEDS) model can naturally resolve the EDE coincidence problem at the background level without any fine tuning of the coupling to dark matter or of the initial conditions. When fitting to current cosmological data, including that from the local distance ladder and the low-redshift amplitude of fluctuations, the tEDS maximum-likelihood model performs comparably to EDE for resolving the Hubble tension, achieving $H_0 =71.2$ km/s/Mpc. However, fitting the \emph{Planck} cosmic microwave background data requires a specific range of initial field positions to balance the scalar field fluctuations that drive acoustic oscillations, providing testable differences with other EDE models.