When the phrase "relatively rapid" is used in relation to the history of the earth, it's a lot longer than you likely assume. The Cambrian explosion is a period which likely lasted 5-10 million (yes, million) years and up to as long as 40 million years. We observed speciation in matters of single digit years. I don't see how that can't happen over 10,000,000 of those years.
Evolutionists attribute the Cambrian explosion to various factors like an increase in oxygen levels in the atmosphere or an after effect of extinction event. In addition, there was a kind of change which was either environmental or physical that caused the growth. Read more, en.wikipedia.org/wiki/Cambrian_explosion.