The smallest geological change necessary to ensure that insufficient fossils exist to create the evolutionary ideas as you requested is: No change at all.
Fossils did not provide the "origin of humanity" idea in the first place
As has already been pointed out, the idea that creatures evolved from common ancestors did not originate with analysis of fossils.
Fossils may already be insufficient to trace the link you speak of
Further, even when fossils came into the equation, they did just as much, if not more, to dismiss modern evolutionary theories as they did to support it. For a long time there was a controversy called "The Missing Link." The argument went something like this (simplified for this answer): You have found fossils of humans, fossils of apes, and fossils of an extinct semi-apelike creature that is our common ancestor, but you have found no fossils that suggest the extinct creature ever evolved into humans.
Indeed, some prominent evolutionists were concerned about this and looked hard for evidence to connect the proposed common ancestors to their modern day descendants. It was even suggested by some of them that, if they fail to find some of the evidences their model suggested should exist, then the modern evolutionary model should be abandoned.
We do have more evidence now. However, the evidence is still not conclusive enough for all scientists to agree. In fact, there is a minority group (but still quite large) of scientists who do not believe that humans and apes have a common animal ancestor from which they both descended.
In science, even among people with the same (or similar) beliefs, there is a lot of argument; scientists do not all hold strong to one unified belief where they are all in concert. Even many of the supporters of the current evolutionary model will suggest that the fossil record as dug up so far is not yet sufficient to trace human origin.
The fossil record we have is enough for the majority of scientists in that field to support the modern evolutionary model, but it is still sufficiently lacking such that a reasonably large portion of reasonable scientists do not support it.
If there are smart, well educated professors and scientists who do not believe that even our current fossil record that we do have in reality is sufficient to make human evolution traceable, to the point where they don't even believe there is a link to be traced, then surely the amount of geological change necessary to suggest such a link is untraceable is zero change.
In fact, I speculate that the modern evolutionary model would still exist today, mostly intact, even if we had no fossils more than a few generations old for study.