The paper examines climate mitigation strategies to reach net-zero emissions by mid-century, focusing on smoothing macroeconomic costs in the short- to medium-term - the horizon relevant for policymakers. It explores a comprehensive policy package, which complements carbon pricing with an initial green fiscal stimulus, consisting of green public investment and subsidies to renewables production. Model simulations show that thanks to the green public spending, the policy package boosts global output relative to the baseline for the first 15 years of the low-carbon transition. Subsequent transitional output costs resulting from further increases in carbon prices are moderate of the order of 1 percent of baseline global GDP by 2050. The findings suggest that upfront green fiscal packages could help smooth the transition to a low-carbon economy. In the current context of the Covid-19 economic crisis, they would help support the recovery from the crisis and put the global economy on a greener, more sustainable path.