I find reconstructions of past global temperatures and carbon dioxide levels such as here to be very interesting from an academic perspective. But attempts to reconstruct temperatures of the geologic past are fraught with assumptions and interpretations of the geologic record driven by presuppositions. The weight of scientific evidence across scientific disciplines does not support dating the age-of-the-earth at billions of years.
However, I do agree with the major point being made here regarding CO2 and temperature. If you believe the past geological timescale temperature reconstruction posted here, and believe that CO2 is somehow mechanistically driving global temperatures, then you clearly have a problem because this particular geologic timescale reconstruction does not support such a position. In any case, since no one was preset in the past to measure actual temperatures and CO2 levels their past levels and correlation (or lack of correlation) is speculative.