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 ∼ 110 and ∼ 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 ≲ 24.1 mag (≲ 23.3) in the B-band (F218W), however evolving over a timescale of ∼ 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 ≲ 26.3 mag (≲ 29.6) assuming all Type Ia gLSNe have a 1 M⊙ 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⊙ main sequence companions at 95% confidence.