  Being the most prominent HI line, Ly$\alpha$ permeates the cosmic web in
emission. Despite its potential as a cosmological probe, its detection on large
scales remains elusive. We present a new methodology to perform Ly$\alpha$
intensity mapping with broad-band optical images, by cross-correlating them
with Ly$\alpha$ forest data using a custom one-parameter estimator. We also
develop an analytical large-scale Ly$\alpha$ emission model with two parameters
(average luminosity $\langle L_{\rm Ly\alpha} \rangle$ and bias $b_{\rm e}$)
that respects observational constraints from QSO luminosity functions. We
compute a forecast for DECaLS/BASS $g$-band images cross-correlated with DESI
Ly$\alpha$ forest data, setting guidelines for reducing images into Ly$\alpha$
intensity maps. Given the transversal scales of our cross-correlation (26.4
arcmin, $\sim$33 cMpc/h), our study effectively integrates Ly$\alpha$ emission
over all the cosmic volume inside the DESI footprint at $2.2 < z < 3.4$ (the
$g$-band Ly$\alpha$ redshift range). Over the parameter space ($\langle L_{\rm
Ly\alpha} \rangle$, $b_{\rm e}$) sampled by our forecast, we find a 3$\sigma$
of large-scale structure in Ly$\alpha$ likely, with a probability of detection
of 23.95\% for DESI-DECaLS/BASS, and 54.93\% for a hypothetical DESI phase II
with twice as much Ly$\alpha$ QSOs. Without a detection, we derive upper bounds
on $\langle L_{\rm Ly\alpha} \rangle$ competitive with optimistic literature
estimates ($2.3 \pm 1 \cdot 10^{\rm 41}$ erg/s/cMpc$^3$ for DESI, and
$\sim$35\% lower for its hypothetical phase II). Extrapolation to the
DESI-Rubin overlap shows that a detection of large-scale structure with
Ly$\alpha$ intensity mapping using next-generation imaging surveys is certain.
[abridged]
