  We explore the interplay of a charge density wave (CDW) order and s-wave
superconductivity (sSC) in a disordered system. Recent experiments on
1T-TiSe_2, where the pristine sample has a commensurate CDW order and the
superconductivity appears upon copper intercalation, motivates our study.
Starting with an extended Hubbard model, with parameters which yield a CDW
ground state within Hartree-Fock-Bogoliubov formalism in pure systems, we show
that the addition of disorder quickly wipes out the global charge order by
disrupting periodic modulation of density at some (low) strength of disorder.
Along with this, the subdominant superconducting order emerges in regions that
spatially anti-correlates with islands of strong local CDW order. The
short-range density modulations, however, continue to persist and show
discernible effects up to a larger disorder strength. The local CDW puddles
reduce in size with increasing disorder and they finally lose their relevance
in effecting the properties of the system. Our results have strong implications
for the experimental phase diagram of transition metal dichalcogenides.
