The habitability of Earth significantly depends on the evolution of its atmospheric properties, which are strongly influenced by escape processes. Polar outflow, which encompasses the atmospheric escape of ions through the open field lines of the Earth's magnetosphere, is the dominant escape process for modern Earth and likely played a significant role in Earth's early history as well. In this article, we investigate the evolution of Earth's polar outflow during the Archean eon 3-4 gigayears (Ga) ago for an N2-CO2 atmosphere. For this, we use a kinetic direct simulation Monte Carlo (DSMC) particle code to simulate the interactions between the solar wind and the Earth's upper atmosphere. We explore the effects of different CO2 mixing ratios (10%, 25%, 50%, 75%, 99%) on the polar outflow escape rates of oxygen, nitrogen and carbon. Using the ion production rates as an estimate for polar outflow, our results indicate that during the time 3.6-4.0 Ga ago, a CO2 mixing ratio larger than 25% may have been necessary to avoid excessive escape via polar outflow. Close to 4 Ga ago, even 50% CO2 may have been necessary due to the stronger solar winds. Our results align with other studies also suggesting a similarly high CO2 mixing ratio in the early Archean.