It absolutely is much harder to make a search engine (at least a good one). The dominance of Google in that space for so long should have made that obvious.

or it makes it obvious that Google has had a monopoly for reasons other than the difficulty of making a search engine (this is the truth.)

That’s bullshit, Google came after a bunch of other worse search engines and ate all of the market share because it was so much better.

If you think they got it some other way, you weren’t using the Internet in the early 2000s

How they took over is a completely different subject from how they maintained dominance.

how exactly do they maintain dominance on the desktop, with Edge / Safari being the default browsers on a new machine ?

that was the point. a car is much easier to make, and they couldn't even do that after 10 years.