  We present the snapshot distance method (SDM), a modern incarnation of a
proposed technique for estimating the distance to a Type Ia supernova (SN Ia)
from minimal observations. Our method, which has become possible owing to
recent work in the application of deep learning to SN Ia spectra (we use the
deepSIP package), allows us to estimate the distance to an SN Ia from a single
optical spectrum and epoch of $2+$ passband photometry -- one night's worth of
observations (though contemporaneity is not a requirement). Using a compilation
of well-observed SNe Ia, we generate snapshot distances across a wide range of
spectral and photometric phases, light-curve shapes, photometric passband
combinations, and spectrum signal-to-noise ratios. By comparing these estimates
to the corresponding distances derived from fitting all available photometry
for each object, we demonstrate that our method is robust to the relative
temporal sampling of the provided spectroscopic and photometric information,
and to a broad range of light-curve shapes that lie within the domain of
standard width-luminosity relations. Indeed, the median residual (and
asymmetric scatter) between SDM distances derived from two-passband photometry
and conventional light-curve-derived distances that utilise all available
photometry is $0.013_{-0.143}^{+0.154}$ mag. Moreover, we find that the time of
maximum brightness and light-curve shape (both of which are spectroscopically
derived in our method) are only minimally responsible for the observed scatter.
In a companion paper, we apply the SDM to a large number of sparsely observed
SNe Ia as part of a cosmological study.
