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How did CO₂ originate on Earth before there was life?
To start life there has to be $\ce{CO2}$.
$\ce{Solar energy + 6CO2 + 6H2O -> C6H12O6 (sugars) + 6O2}$
$C_6H_{12}O_{6} + O_2 \longrightarrow H_2O + {CO}_2 + \text{Energy}$
So to start this cycle, ...