  We introduce a machine learning method for estimating the sensitivity of
strong lens observations to dark matter subhaloes in the lens. Our training
data include elliptical power-law lenses, Hubble Deep Field sources, external
shear, and noise and PSF for the Euclid VIS instrument. We set the
concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$
relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$
simulated strong lens observations with depth and resolution resembling Euclid
VIS images. We find that, with a $3\sigma$ detection threshold, $2.35$ per cent
of pixels inside twice the Einstein radius are sensitive to subhaloes with a
mass $M_\mathrm{max}\leq 10^{10}M_\odot$, $0.03$ per cent are sensitive to
$M_\mathrm{max}\leq 10^{9}M_\odot$, and, the limit of sensitivity is found to
be $M_\mathrm{max}=10^{8.8\pm0.2}M_\odot$. Using our sensitivity maps and
assuming CDM, we estimate that Euclid-like lenses will yield
$1.43^{+0.14}_{-0.11}[f_\mathrm{sub}^{-1}]$ detectable subhaloes per lens in
the entire sample, but this increases to
$35.6^{+0.9}_{-0.9}[f_\mathrm{sub}^{-1}]$ per lens in the most sensitive
lenses. Estimates are given in units of the inverse of the substructure mass
fraction $f_\mathrm{sub}^{-1}$. Assuming $f_\mathrm{sub}=0.01$, one in every
$70$ lenses in general should yield a detection, or one in every $\sim$ three
lenses in the most sensitive sample. From $170,000$ new strong lenses detected
by Euclid, we expect $\sim 2500$ new subhalo detections. We find that the
expected number of detectable subhaloes in warm dark matter models only changes
relative to cold dark matter for models which have already been ruled out,
i.e., those with half-mode masses $M_\mathrm{hm}>10^8M_\odot$.
