  We put constraints on the epoch of dark matter formation for a class of
non-WIMP (Weakly Interacting Massive Particle) dark matter candidates. These
models allow a fraction of Cold Dark Matter (CDM) to be formed between the
epoch of Big Bang Nucleosynthesis (BBN) and the matter radiation equality. We
show that for such models the matter power spectra might get strong suppression
even on scales that could be probed by linear perturbation theory at low
redshifts. Unlike the case of Warm Dark Matter (WDM), where the mass of the
dark matter particle controls the suppression scale, in Late Forming Dark
Matter (LFDM) scenario, it is the redshift of the dark matter formation which
determines the form of the matter power spectra. We use the Sloan Digital Sky
Survey (SDSS) galaxy clustering data and the linear matter power spectrum
reconstructed from the Lyman-$\alpha$ data to find the latest epoch of the dark
matter formation in our universe. If all the observed dark matter is late
forming, we find lower bounds on the redshift of dark matter formation $z_f >
1.08 \times 10^5 $ at 99.73 $\%$ C.L from the SDSS data and $z_f > 9 \times
10^5$, at the same C.L, from the Lyman-$\alpha$ data. If onlya fraction of the
dark matter is late forming then we find tentative evidence of the presence of
LFDM from the Lyman-$\alpha$ data. Upcoming data from SDSS-III/BOSS (Baryon
Oscillation Spectroscopic Survey) will allow us to explore this issue in more
detail.
