Owing to its unique geometry, the kagome lattice hosts various many-body quantum states including frustrated magnetism, superconductivity, charge-density waves (CDWs), and topologically nontrivial phases of matter. Kagome metals with 2×2 CDWs, corresponding to the nesting of van Hove saddle points, are found to exhibit a number of exotic electronic phases, and have been the focus of much recent research. More recently, a √3×√3 CDW was discovered in the kagome metal ScV6Sn6 below TCDW≈91 K, whose underlying mechanism and formation process remain unclear, particularly in comparison with the 2×2 kagome CDWs. Using inelastic X-ray scattering, we discover a short-range √3×√3×2 CDW that is dominant in ScV6Sn6 well above TCDW, distinct from the √3×√3×3 CDW below TCDW. The short-range CDW grows upon cooling, and is accompanied by the softening of phonons, indicative of its dynamic nature. As the √3×√3×3 CDW appears, the short-range CDW becomes suppressed, revealing a competition between these CDW instabilities. The competing CDW instabilities in ScV6Sn6 lead to an unusual CDW formation process, with the most pronounced phonon softening and the static CDW occurring at different wavevectors. Our first-principles calculations indicate that the √3×√3×2 CDW is energetically favored, consistent with experimental observations at high temperatures. However, the √3×√3×3 CDW is selected as the ground state due to a large wavevector-dependent electron-phonon coupling (EPC), which also accounts for the enhanced electron scattering above TCDW. Our findings reveal the dominance of EPC-driven correlated many-body physics in ScV6Sn6, making it an ideal system to study emergent quantum matter in the strong EPC regime.