We present a physically motivated model of dark energy (DE) rooted in the topological structure of the Quantum Chromodynamics (QCD) vacuum. In this framework, DE arises from the difference between the QCD vacuum energy in an expanding Universe and in Minkowski spacetime, with the relevant contribution generated by tunnelling between distinct topological sectors. The QCD scale, $\Lambda_{\rm QCD}\sim100,{\rm MeV}$, naturally produces a vacuum-energy density of the same order of magnitude as the observed one, without introducing new fundamental fields, couplings, or fine-tuning. We show that the same mechanism can naturally accommodate an evolving dark-energy component. The resulting effective equation-of-state parameter $\omega_{\rm DE}$ can evolve with redshift, lie on either side of $-1$, and cross the $\omega_{\rm DE}=-1$ boundary, while asymptotically approaching $-1$ in the future. The framework offers a common physical origin for both the small amplitude of dark energy and its possible time evolution, the latter being suggested by recent DESI observations. Here, we develop the physical and cosmological aspects of the framework; its confrontation with cosmological data is presented in a companion paper.