It is populations that evolve, not individuals.
Let me give an example
East to West Squirrels
OK, we have lotso squirrels living all over the place from east to west. Small, but no vast empty spots (deserts, mountains).
Squirrels don’t migrate and don’t wander far from home. Mutations that occur in the east just keep piling up, as do all the others all the way to the west, but the extreme eastern ones and the extreme western ones are different.
So, eventually, the western squirrels are larger, mate only in the dry season, have black tails, etc. The eastern squirrels are smaller, have grey tails, but black ears, mate only in the fall and gestate during hiberation.
Because of the size difference they cannot mate successfully. New species
LOL!
Then presumably Shetland ponies and Clydesdales belong to different species.
And Chihuahuas and Great Danes are also different species too.
So your theory is that the genetic mutations that are random occur simultaneously throughout a population, and that the new species is birthed multiple times within years of each other so that breeding and replication can continue.
Despite your population theory, logic tells you that at some point a single individual representing the new species is birthed. You still have not addressed the major issue at stake.