Photometric stellar surveys now cover a large fraction of the sky, probe to fainter magnitudes than large-scale spectroscopic surveys, and are relatively free from the target selection biases often associated with such studies. Photometric-metallicity estimates that include narrow/medium-band filters can achieve comparable accuracy and precision to existing low-resolution spectroscopic surveys such as Sloan Digital Sky Survey/SEGUE and LAMOST. Here we report on an effort to identify likely members of the Galactic disk system among the very metal-poor (VMP; [Fe/H]{<=}-2) and extremely metal-poor (EMP; [Fe/H]{<=}-3) stars. Our analysis is based on an initial sample of ~11.5 million stars with full space motions selected from the SkyMapper Southern Survey (SMSS) and Stellar Abundance and Galactic Evolution Survey (SAGES). After applying a number of quality cuts to obtain the best available metallicity and dynamical estimates, we analyze a total of ~5.86 million stars in the combined SMSS/SAGES sample. We employ two techniques that, depending on the method, identify between 876 and 1476 VMP stars (6.9%-11.7% of all VMP stars) and between 40 and 59 EMP stars (12.4%-18.3% of all EMP stars) that appear to be members of the Galactic disk system on highly prograde orbits (V_{phi}_>150km/s). The total number of candidate VMP/EMP disklike stars is 1496, the majority of which have low orbital eccentricities, ecc<=0.4; many have ecc<=0.2. The large fractions of VMP/EMP stars associated with the Milky Way disk system strongly suggest the presence of an early-forming "primordial" disk.