Early in the Covid-19 outbreak, it was speculated that pre-existing cross-reactive immunity from prior BCG vaccination or exposure to common cold human coronaviruses might confer some protection against Covid-19. Following a year of circulation of SARS-CoV-2 through the world, epidemiological dynamics allow a test of this hypothesis. A dynamic epidemiological model was fitted to the Covid-19 attributed ‘excess deaths’ in South Africa, a country with a long-standing BCG vaccination program and where social-economic circumstances potentially result in frequent exposure to common cold coronaviruses. We show that Covid-19 propagation dynamics in South Africa are consistent with an initially fully susceptible population (no prior cross-immunity protecting against infection), but this requires assuming values of the infection fatality rate (IFR) below or at the lower plausible range (0.31 to 0.53) of internationally reported values. This suggests that some form of pre-existing protection against severe Covid-19 may exist in South Africa. The observed disease propagation dynamics can be explained by both long-lasting immunity and various scenarios of reinfection in the presence of the more transmissible B.1.351 variant, which is also relatively resistant to antibodies induced by infections of prototype SARS-CoV-2. All scenarios of reinfection also require assuming a low IFR in order to replicate the observed attributes of the outbreak.