We present an energy transition pathway constrained by a total CO2 budget of 7 Gt allocated to the German energy system after 2020, the Budget Scenario (BS). We apply a normative backcasting approach for scenario building based on historical data and assumptions from existing scenario studies. The modeling approach combines a comprehensive energy system model (ESM) with REMix—a cost optimization model for power and heat that explicitly incorporates sector coupling. To achieve the necessary CO2 reduction, the scenario focuses on electrifying all end use sectors until 2030, adding 1.5–2 million electric vehicles to the road per year. In buildings, 400,000–500,000 heat pumps would be installed annually by 2030, and the share of district heating would double until 2050. In the scenario, coal needs to be phased out by 2030. Wind and Photovoltaic (PV) capacities would need to more than double to 290 GW by 2030 and reach 500 GW by 2050. The BS results indicate that a significant acceleration of the energy transition is necessary before 2030 and that this higher pace must be maintained thereafter until 2050.