While those mechanisms are involved the current theory is that usually a population becomes genetically isolated first. The larger and more genetically diverse a population is, the more resistant it is to “evolutionary noise” which keeps the genetics stable because there aren’t many mutations or ecological changes that give one group within a species significant advantages over another. It’s not until the relevant population is reduced that mutations and other factors have strong effects (usually) that can cause speciation.

How that isolation happens varies and can take a single generation or up to hundreds of thousands of years. A polyploid plant, for example, might become genetically isolated within a single generation or a homoploid hybrid within a few generations by losing reproductive compatibility with the rest of its species. Then a mutation might give it significant advantages without making it into the rest of the population or a “sudden” ecological change favors the new population over the old, giving the new one room to grow and outcompete.

Other species are isolated over “short” periods via flooding, rising mountains, changes in the paths of rivers, expansion of a predator’s range, fires, and so on. Anything that can isolate a small group of a species geographically can also create a speciation event.

Nature has one thing most evolutionary algorithms don't: environmental changes. That has a way of stirring up the pot.

Which is not at all to say that you're wrong. A lot of the known major environmental changes were brought upon by other creatures - sometimes creatures that found some weird new way of doing things, and upended the environment with it.