I agree very much with you, there's definitely a moment where one earns a cats trust, it might take days, it might take months or even years perhaps but there certainly is such a moment. All mine are different, with Alfie it took a few weeks before he fully settled in and I earned, yes I think earned is the appropriate word, his trust and this trust has grown ever since. When I got him he was pretty nervous and a tickle of the tummy or a touch of his legs earned a swift claws-out swipe in return, but that all changed and now he's a "pussy cat" if you excuse the expression
and he'll invite me to stroke his tummy etc. at the drop of a hat. Frankie settled very quickly after only a few days, as he came from a 13 cat household where I suppose he didn't get much, if any, individual attention it didn't take him long to realise that "this is a good thing, I've got a lap pretty much to myself, I don't have to fight for food and a warm place to curl up and sleep, marvellous, yes sir, I'll have some of this this thank you very much!"
. Suzie, my mum's 17 YO cat who I adopted last year was very frightened by the change of scenery, she used to sleep behind my head on the pillow and avoid the others and hiss at them but she's settled in eventually and is so affectionate to me that she'd be only too happy if I spent 24 hours a day in bed so that she had my constant attention and affection instead of which she only has me to herself for a megre 9 hours a day
Cheers
Leigh
