We compare the health and economic costs of early and delayed mandated suppression and the unmitigated spread of ‘first-wave’ COVID-19 infections in Australia in 2020. Using a fit-for-purpose SIQRM-compartment model for susceptible, infected, quarantined, recovered and mortalities on active cases, that we fitted from recorded data, a value of a statistical life year (VSLY) and an age-adjusted value of statistical life (A-VSL), we find that the economic costs of unmitigated suppression are multiples more than for early mandated suppression. We also find that using an equivalent VSLY welfare loss from fatalities to estimated GDP losses, drawn from survey data and our own estimates of the impact of suppression measures on the economy, means that for early suppression not to be the preferred strategy requires that Australia would have to incur more than 12,500–30,000 deaths, depending on the fatality rate with unmitigated spread, to the economy costs of early mandated suppression. We also find that early rather than delayed mandated suppression imposes much lower economy and health costs and conclude that in high-income countries, like Australia, a ‘go early, go hard’ strategy to suppress COVID-19 results in the lowest estimated public health and economy costs.