How was it possible that CO2 levels were higher nearly 650,000 years ago?
The explanation is that human activities are not the only processes that affect atmospheric composition.  

Last time CO2 levels were higher than today was 10-15 million years, during the Miocene epoch. During the Miocene, sea level estimated to be 100 feet higher and the global average surface temperature estimated to be 10°F warmer than today.





References:

Miocene Sea level graph.

Temperature over time graph.

www.climatecentral.org

Coupling of CO2 and Ice Sheet Stability Over Major Climate Transitions of the Last 20 Million Years