Recent results from the Dark Energy Spectroscopic Instrument (DESI) provide mounting evidence that dark energy is dynamical, exhibiting mild time evolution rather than remaining a pure cosmological constant. Motivated by these observations, we introduce a simple scalar-field model in which the coupled dark-energy/dark-matter sector acts as a slowly accumulating "static charge." Vacuum energy density builds in a metastable false-vacuum state until a critical threshold triggers quantum tunneling (Coleman—De Luccia bubble nucleation) or extra-dimensional leakage, discharging the accumulated energy and nucleating a new bubble universe. We derive an explicit time-dependent nucleation rate Γ(t) ∝ t^−β (β ≈ 2) arising from Hubble suppression in the early, denser universe, naturally producing fewer discharges per horizon volume ∼10 Gyr ago and a higher relative rate in the present epoch. Monte-Carlo simulations of the process demonstrate that successive bubble-universe births exhibit hierarchical scaling: each child universe inherits a mass/energy budget smaller by 1—3.5 orders of magnitude relative to its parent, consistent with fractional tunneling leakage. The mechanism yields a distinctive stochastic gravitational-wave background (SGWB) generated by bubble collisions, sound waves, and turbulence. The spectrum features a softened infrared tail and a secondary mHz hump whose amplitude and shape are uniquely tied to the time-dependent discharge history. This signal lies within the projected sensitivity of LISA (core band ∼1—10 mHz) and pulsar-timing arrays (low-frequency shoulder), offering a concrete, multi-messenger test. Future DESI releases and next-generation gravitational-wave observatories can therefore falsify or support the charge-discharge picture as a dynamical channel for bubble-universe formation in a hierarchical multiverse.