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.
Vargas Zeppetello, L. R., Donohoe, A., & Battisti, D. S. (2019). Does surface temperature respond to or determine downwelling longwave radiation? Geophysical Research Letters, 46, 2781–2789. https://doi.org/10.1029/2019GL082220
Downward longwave radiation (DLR) is often assumed to be an independent forcing
on the surface energy budget in analyses of Arctic warming and land-atmosphere interaction. We use radiative kernels to show that the DLR response to forcing is largely determined by surface temperature perturbations. We develop a method by which vertically integrated versions of the radiative kernels are combined with surface temperature and specific humidity to estimate the surface DLR response to greenhouse forcing. Through a decomposition of the DLR response, we estimate that changes in surface temperature produce at least 63% of the clear-sky DLR response in greenhouse forcing, while the changes associated with clouds account for only 11% of the full-sky DLR response. Our results suggest that surface DLR is tightly coupled to surface temperature; therefore, it cannot be considered an independent component of the surface energy budget.