Check out this topic I made previously : https://forum.inaturalist.org/t/useful-casual-observations-being-hidden-by-other-low-grade-casual-observations/36089
Although we do not have a fossil section of iNaturalist, we can always add Observation Field of Fossil (yes or no, so click yes), and with that, we can gather fossil observations using projects. I think this is the best we can do, since in general iNat do not encourage people to post fossils.
Also, when you post or see fossil observations, please make sure to mark “Evidence of recent organism” section in Data Quality Assignment as “No”, so we can make sure that fossils do not appear on distribution maps.