  We determine the viability of exploiting lensing time delays to observe
strongly gravitationally lensed supernovae (gLSNe) from first light. Assuming a
plausible discovery strategy, the Legacy Survey of Space and Time (LSST) and
the Zwicky Transient Facility (ZTF) will discover $\sim$ 110 and $\sim$ 1
systems per year before the supernova (SN) explosion in the final image
respectively. Systems will be identified $11.7^{+29.8}_{-9.3}$ days before the
final explosion. We then explore the possibility of performing early-time
observations for Type IIP and Type Ia SNe in LSST-discovered systems. Using a
simulated Type IIP explosion, we predict that the shock breakout in one
trailing image per year will peak at $\lesssim$ 24.1 mag ($\lesssim$ 23.3) in
the $B$-band ($F218W$), however evolving over a timescale of $\sim$ 30 minutes.
Using an analytic model of Type Ia companion interaction, we find that in the
$B$-band we should observe at least one shock cooling emission event per year
that peaks at $\lesssim$ 26.3 mag ($\lesssim$ 29.6) assuming all Type Ia gLSNe
have a 1 M$_\odot$ red giant (main sequence) companion. We perform Bayesian
analysis to investigate how well deep observations with 1 hour exposures on the
European Extremely Large Telescope would discriminate between Type Ia
progenitor populations. We find that if all Type Ia SNe evolved from the
double-degenerate channel, then observations of the lack of early blue flux in
10 (50) trailing images would rule out more than 27% (19%) of the population
having 1 M$_\odot$ main sequence companions at 95% confidence.
