  We present the first discoveries from a survey of $z\gtrsim6$ 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 $z\gtrsim7$ and to conduct a complete census of
the faint quasar population at $z\gtrsim6$. In this paper, we report on the
selection method of our search, and on the initial discoveries of two new,
faint $z\gtrsim6$ quasars and one new $z=6.63$ quasar in our pilot
spectroscopic observations. The two new $z\sim6$ 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 $z\gtrsim6$. 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 $z\gtrsim7$
quasars. Extrapolating from previous QLF measurements, we predict that these
combined datasets will yield $\sim200$ $z\sim6$ quasars to $z_{\rm AB} < 21.5$,
$\sim1{,}000$ $z\sim6$ quasars to $z_{\rm AB}<23$, and $\sim 30$ quasars at
$z>6.5$ to $J_{\rm VEGA}<19.5$.
