On the other hand, you can't very well call your assumption "evidence" for an old earth. An assumption is not evidence.
Lack of evidence is not proof but it IS evidence.
If there are no symptoms that I am ill, it is evidence that I am healthy, but not proof, because maybe I have cancer and just don't have any symptoms. But unless I am a hypochondriac I am going to assume I am healthy.
Lack of evidence for a cataclysmic event means it is safe to assume that the event did not occur. This is an even safer assumption then me assuming I am healthy because cataclysmic events leave evidence. That is sort of the definition of cataclysmic.