The formation of flat electronic bands from long-wavelength superperiodic moiré potentials in van der Waals heterostructures underpins the creation and control of a host of highly-tunable correlated and topological phases. While the underlying moiré periodicity is typically a fixed property of the heterostructure, here we show how the development of a charge-density wave (CDW) in one of the constituent materials can create an emergent moiré lattice. We demonstrate this experimentally in TiSe₂/graphite epitaxial heterostructures, using angle-resolved photoemission and scanning-tunnelling microscopy and spectroscopy to directly image the resulting long-wavelength moiré potential and concomitant flat-band formation. We show how the intrinsically low-energy, deformable landscape of the CDW imparts significant tunability, stabilising quasi-one-dimensional moiré domains from symmetry breaking within the CDW, and allowing the complete suppression of flat-band formation by carrier doping across the CDW phase transition. Our findings thus open a new avenue for engineering moiré matter by exploiting the rich many-body states of the parent compounds of 2D heterostructures.