We present the first discoveries from a survey of $zgtrsim6$ 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 deg$^2$ of sky down to $z_{rm AB}sim23.0$, and UKIDSS and UHS, which will map the northern sky at $0<DEC<+60^{circ}$, reaching $J_{rm VEGA}sim19.6$ (5-$sigma$). The combination of these datasets allows us to discover quasars at redshift $zgtrsim7$ and to conduct a complete census of the faint quasar population at $zgtrsim6$. In this paper, we report on the selection method of our search, and on the initial discoveries of two new, faint $zgtrsim6$ quasars and one new $z=6.63$ quasar in our pilot spectroscopic observations. The two new $zsim6$ quasars are at $z=6.07$ and $z=6.17$ with absolute magnitudes at rest-frame wavelength 1450 AA 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 $zgtrsim6$. 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 datasets to find $zgtrsim7$ quasars. Extrapolating from previous QLF measurements, we predict that these combined datasets will yield $sim200$ $zsim6$ quasars to $z_{rm AB} < 21.5$, $sim1{,}000$ $zsim6$ quasars to $z_{rm AB}<23$, and $sim 30$ quasars at $z>6.5$ to $J_{rm VEGA}<19.5$.
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