How did the domestic cat evolve? I am going to answer this without reference to anyone’s work. Anyone is free to add information in comments.
The first domestic cat was a North African wild cat and domestication happened around 10,000 years ago in or near Cyprus. This small wildcat is quite naturally predisposed to being domesticated. They are still domesticated in Africa.
When there are many unsterilised domesticated wild cats – as they all were in those days – they mate and create offspring. The offspring would have been born into homes because the parents were domesticated.
Whereas their parents were true wild cats living mainly outside the home, their offspring and subsequent kittens would have lived in the home and been fed by humans often in relatively urban environments as opposed to farm environments in the early days of domestication.
There would be inbreeding and this would allow recessive genes to take effect changing appearance, and there would mutations over eons which would lead to new appearances.
New naturally occurring ‘breeds’ of domestic cat would have been created such as the Manx (tailless) because a group of cats live in isolation i.e. the cats were isolated from other members of the same species. An example of a current informal breed is the Bahraini Dilmun.
Essentially the differences in appearance of the domestic cat is due to mutations occurring naturally and the ‘founder effect’. The founder effect is the loss of genetic variation when a population of cats is created by relatively few individuals due to isolation.
Ten thousand years is long enough for a significant amount of evolution to take place which accounts for the change in appearance of the first domestic cats being African wild cats (which look like tabby cats) to the wide variety of cat coats and body conformations that we see today.
To that you can add deliberate selective breeding by cat breeders to create new breeds which exaggerates domestic cat appearance.
Nearly all cats are random bred. These cats breed without human interference. However, they do select their partners for mating. Amongst domestic cats this would have created cats that were more suited to domestic life because they needed to be suited to that way of life. I’d expect unsuited domestic cats to have been cast out by their human caretaker or not brought in as domestic cats. This would have strengthened the domestic cat’s appearance and behaviour over thousands of years.
International traders and ship’s cats would have spread the domestic cat to all corners of the world from their place of origin, the Fertile Crescent which is where modern Syria is now situated.
And so the domestic cat evolved. Today’s domestic cats are smaller than the N. African wild cat, their jaws are shorter, their brains smaller, their adrenal glands are smaller (less predisposed to flight or fight), their intestines are longer in adapting to being fed by people, their memories are better, and they are more trainable.
The domestic’s inherent behaviour is still close to the N. African wildcat. And their skull shape is similar. The wild cat ancestor is near the surface of the domestic cat.