Sorry, but the ruin periods of earth's history eliminates the possibility of millions of years of uninterrupted evolution.
No one said it was uninterrupted.
The history shows, it goes through periods of rapid acceleration, and periods where almost nothing happens. The technical term is "saltatory", there is a literature on it, you can look it up.
The sudden appearance in the geologic record of new organisms also supports this as well.
Why would you expect organism to appear in a "not sudden" manner? For example - think about the Covid virus. There have been 600 variants catalogued since it was first discovered. Only a dozen of them are deadly, therefore those are the only ones we hear about. And, only the deadly ones get a chance to replicate through the population and leave enough evidence that they were around - but all the other ones existed too, just in smaller numbers (they were "less successful" in terms of evolution because they couldn't find an appropriate host).
So if you were an outsider looking in, what you'd see is one wave of infections from variant A, followed by some quiet time, followed by another wave of infections from variant B. Which is pretty much what we see, right? No one cares about the hundreds of unsuccessful variants that occurred in the meantime, they lived for a short while, couldn't find a host, and became extinct.