(btw as AdminNosy may I now changet the topic title to something like "Dealing with Large Numbers" ? )
A small nit, the billions are, of course a problem for all of us. However, most of the evolutionary history shows pretty darned interesting things happening in millions of years. A bit more graspable but still a problem.
I think you are right about the problem of "wrapping our heads around" such quantities but I think there is more to it than that.
Dwarfing the billions of years are the truely
huge number of events that take place. If a species (like a mouse with at least on generation a year) has a population of millions then in a scant millenium a billion different "tries" take place in the evolutionary dance. In a million years there are a
trillion different individuals each with some change and a different chance at being selected or not.
If there are 10 million species (perhaps a low number) extant at any one time then in a million years there might be over a "sextillion" (this is getting silly) different individuals.
It is the difficulty of being able to imagine what can happen when there are so many "events" occuring each contributing to the evolutionary process that makes it hard for anyone to understand the developmental power of evolution.
These numbers start to dwarf some as small as a silly little billion.