We report a timing analysis of near-infrared (NIR), X-ray, and submillimeter data during a 3 day coordinated campaign observing Sagittarius A*. Data were collected at 4.5um with the Spitzer Space Telescope, 2-8keV with the Chandra X-ray Observatory, 3-70keV with NuSTAR, 340GHz with ALMA, and 2.2um with the GRAVITY instrument on the Very Large Telescope Interferometer. Two dates show moderate variability with no significant lags between the submillimeter and the infrared at 99% confidence. A moderately bright NIR flare (F_K_~15mJy) was captured on July 18 simultaneous with an X-ray flare (F_2-10keV_~0.1counts/s) that most likely preceded bright submillimeter flux (F_340 GHz_~5.5Jy) by about 34_-33^+14^ minutes at 99% confidence. The uncertainty in this lag is dominated by the fact that we did not observe the peak of the submillimeter emission. A synchrotron source cooled through adiabatic expansion can describe a rise in the submillimeter once the synchrotron self-Compton NIR and X-ray peaks have faded. This model predicts high GHz and THz fluxes at the time of the NIR/X-ray peak and electron densities well above those implied from average accretion rates for Sgr A*. However, the higher electron density postulated in this scenario would be in agreement with the idea that 2019 was an extraordinary epoch with a heightened accretion rate. Since the NIR and X-ray peaks can also be fit by a nonthermal synchrotron source with lower electron densities, we cannot rule out an unrelated chance coincidence of this bright submillimeter flare with the NIR/X-ray emission.