I am an environmental geologist, and while I’m not going to debunk or refute the paper or author (someone more up on their game than me can), I will say that the lack of historic data was always a variable that could be reliably solved for eventually. Our fossil evidence and understanding of global tectonics was already allowing it to be unraveled back when I was in college 20 years ago.
So from a modeling standpoint, if you can repeatedly replicate what you know conditions were like in the non-ice/warm periods, you can reliably infer what the CO2 (or just overall greenhouse gas mixtures) had to have been (I won’t get into why we know it was like that, paleontologists will talk your ear off about it any day)! From there you can develop models with very robust and accurate inputs to predict how long it will take to reach those levels at current pace. Every year the trend line gets more and more granular as well because we have so much data.
Idk if/how that impacts this particular study, but it should give OP some background and trust in the modeling that’s based on data we don’t/didn’t have.
You don’t trust “the data” but can’t articulate anything on the subject whatsoever indicating you’ve never as much as looked at “the data” that you’re skeptical of. Or narrow down what aspect of “the data” you don’t trust. Or what methodology makes you skeptical of “the data”. Or what research method was used in obtaining “the data”. Or the repeatability of the experiments being used to test “the data.” Or the peer reviewing of “the data”. Or the credibility of the publishers of “the data”.
You sound like someone that doesn’t have the first clue how any of “the data” is generated, so instead of educating yourself or actually digging in to any of it, you blanket disregard it as untrustworthy.