The definition of optimal COVID-19 mitigation strategies remains worldwide on the top of public health agendas, particularly when facing a second wave. It requires a better understanding and a refined modelling of its dynamics. We emphasise the fact that epidemic models are phenomenologically based on the paradigm of a cascade of contacts that propagates infection. However, the introduction of ad-hoc characteristic times and corresponding rates spuriously break their scale symmetry.Here we theoretically argue and empirically demonstrate that COVID-19 dynamics, during both growth and decline phases, is a cascade with a rather universal scale symmetry whose power-law statistics drastically differ from those of an exponential process. This involves slower but longer phases which are furthermore linked by a fairly simple symmetry. These results explain biases of epidemic models and help to improve them. Due to their generality, these results pave the way to a renewed approach to epidemics, and more generally to growth phenomena.