I think you're missing a few possible scenarios.

First and foremost, cats have exceptional olfactory senses.

Second of all, the mouse was likely moving around before it noticed your cat approaching, at which point it froze. (By that time, it was of course too late.) Mice don't typically just sit in a garden, never moving.

The mouse wasn't moving that you could see. Consider that a mouse has a much higher heart rate; if you can pick one up (eg those rare occasions where you are able to rescue prey from the cat) they practically vibrate in your hand.

Also, another poster makes a good point about cats' hearing. Not only do cats hear in higher frequency ranges than we do thanks to their reduced size, they can angle their ears to 'focus' on a particular sound; being a sound engineer by profession, I desperately envy them this ability. I have simulated this using cardioid microphones while wearing headphones, and I would cheerfully sacrifice a good deal of social standing for a pair of working prehensile ears.

Those pointy ears are there for a reason - cats use more than sight to locate prey.

Their visual acuity isn't based on movement, like a Tyrannosaurus. If you look at a painting, you can still see it just fine even though it's not moving.