The larger than expected discrepancy between values of the Hubble-Lemaitre constant, among those measured by various seemingly independent methods, has been called as a ‘crisis’ in Cosmology. By incorporating the time variance of recession velocities, we present an alternative model for the velocity-distance data of Type Ia supernovae, which can potentially explain the discrepancy between the various independent measurements of the Hubble-Lemaitre constant as well as possibly throw some light on the classically counter-intuitive accelerating expansion of the Universe. This model also gives a possible direct observational evidence for Inflation and Reheating. The idea at its fundamental level is this: The velocity-distance data for Type Ia Supernovae have been traditionally plotted to pass through origin. This models an accelerating Universe as conventionally concluded. However, when we allow for an intercept in the velocity-distance plot, in other words when we allow for an extra-Hubble-Lemaitre (eHL) velocity, we, interestingly, potentially resolve the following four long-persisting intrigues: 1. 'Crisis in Cosmology': Allowing for an eHL velocity also allows us to model the rate of expansion as measured by the Planck collaboration thus removing the existing 'tension' between values of the Hubble-Lemaitre constant. 2. Counter-intuitive accelerating expansion of the Universe: It turns out, interestingly, that allowing for eHL velocities in the model turns the observational data for accelerating expansion into one for decelerating expansion. How this happens is explained in detail in the section titled: ‘Decelerating Universe?’ 3. Accounting for time dependence of observed recession velocities: The classical equation for the observed recession velocity, , neglects its dependence on time. Allowing for an eHL velocity also allows us to include the potential effects of time, which is expected to cause the recession velocities to reduce in a classical Universe dominated by gravity over Dark Energy. Interestingly, this prediction is confirmed by observations as illustrated in the section titled ‘Nature of the eHL velocity’ and Figure 4. 4. Direct observational evidence for reheating and inflation: Allowing for eHL velocities also permits it to be a potential direct remnant of explosive particle creation during reheating and inflation. Such a direct observational evidence was long sought by the Astronomy community.