I miss my Sony DSC U20 from 2004 or so. The focusing was really good for some reason - you could just point it randomly, press the button and it would instantly take a well focused picture unlike modern phone cameras that tend to wait a few seconds and then get it wrong. (https://www.amazon.co.uk/Sony-Cybershot-DSC-U-Digital-Camera...). They weren't very long lived though - most seemed to pack up in a few years.
That camera (and a lot of similar cameras from around then) is fixed focus, so there's no focus delay, but you also can't adjust the focus either. With a fixed focus camera usually everything farther away than X is going to show up in focus (or nearly so) and anything closer isn't going to be in focus. But a lot of the time, you will be at least X away to frame your shot anyway, so no big deal.
Whoops, somebody put wrong info on the US amazon page[1] I had skimmed.
"The DSC-U20 offers a fixed-focus 5mm f2.8 lens"
Of course if I had read a bit more, it does mention autofocus in the next sentence. So anyway, that's not why it's fast then. Sorry for the misdirection.