A route to supercontinuum generation in gas-filled hollow-core anti-resonant fibers is demonstrated through the creation of a broad vibrational Raman frequency comb followed by continuous broadening and merging of the comb lines through either rotational Raman scattering or the optical Kerr effect. The demonstration experiments, utilizing a single pump pulse with 20 ps duration at 532 nm in a nitrogen-filled fiber, produce a supercontinuum spanning from 440 to 1200 nm, with an additional deep ultraviolet continuum from 250 to 360 nm. Numerical results suggest that this approach can produce even broader supercontinuum spectra extending from the ultraviolet to mid-infrared.