Daily rates of infections and deaths collected in several countries during the first SARS-CoV2 (COVID-19) pandemic are approximated by Gaussian functions of the time elapsed since the dates of first occurrence in each country. This representation reveals designating consistently the time evolution of the country-specific daily rates and of the corresponding total duration of the epidemic. Moreover, the appropriate choice of scale units transforms case numbers and time instances to dimensionless quantities and leads to condensing data from twenty-three countries on two master Gaussian curves (infections/deaths). Thereby, data deviations from the average Gaussian behavior are quantified via error bars integrating the effects of local epidemic specificities, of counting errors and of low statistics. The Gaussian master representation helps fixing unambiguously the epidemic peaks and anticipates the duration of the epidemic while discriminating country data that abnormally depart from the average behavior. Finally, this method builds a basis for investigating the evolution of the epidemic in different countries and for establishing comparisons between country-specific public health policies.