Part of what makes this kind of thing difficult to really fathom is the time scales involved - e.coli can reproduce once every 20min or so, yeast can do so ever

Part of what makes this kind of thing difficult to really fathom is the time scales involved - e.coli can reproduce once every 20min or so, yeast can do so every 2 hours or so. 12 replications a day, 4380 replications per year, repeated over a billion years. It all seems phenomenally unlikely, but the combination of an unfathomable number of repetitions and even a small evolutionary thumb on the scale can take you an enormous distance.