We present the first discoveries from a survey of z ≳ 6 quasars using imaging data from the DECam Legacy Survey (DECaLS) in the optical, the UKIRT Deep Infrared Sky Survey (UKIDSS) and a preliminary version of the UKIRT Hemisphere Survey (UHS) in the near-IR, and ALLWISE in the mid-IR. DECaLS will image 9000 deg2 of sky down to z AB ∼ 23.0, and UKIDSS and UHS will map the northern sky at 0 < decl. < +607deg;, reaching J VEGA ∼ 19.6 (5-σ). The combination of these data sets allows us to discover quasars at redshift z ≳ 7 and to conduct a complete census of the faint quasar population at z ≳ 6. In this paper, we report on the selection method of our search, and on the initial discoveries of two new, faint z ≳ 6 quasars and one new z = 6.63 quasar in our pilot spectroscopic observations. The two new z ∼ 6 quasars are at z = 6.07 and z = 6.17 with absolute magnitudes at rest-frame wavelength 1450 Å being M 1450 = -25.83 and M 1450 = -25.76, respectively. These discoveries suggest that we can find quasars close to or fainter than the break magnitude of the Quasar Luminosity Function (QLF) at z ≳ 6. The new z = 6.63 quasar has an absolute magnitude of M 1450 = -25.95. This demonstrates the potential of using the combined DECaLS and UKIDSS/UHS data sets to find z ≳ 7 quasars. Extrapolating from previous QLF measurements, we predict that these combined data sets will yield ∼200 z ∼ 6 quasars to z AB < 21.5, ∼1000 z ∼ 6 quasars to z AB < 23, and ∼30 quasars at z > 6.5 to J VEGA < 19.5.