Is there a low-cost camera that doesn't have the slow start-up of the ov2640?

I am designing a wifi camera that needs to power on and take a picture in one second. I have spent some time with an esp32-cam and ov2640 and finally realized the auto-exposure on the ov2640 made the camera start-up time about 7 seconds when using the UXGA that I need.

I’ve tried a number of things, like starting with low-resolution for a few frames, but then I was unable to update the resolution after that.

I have also discovered the esp32-cam doesn’t support anything other than the ov2640 because of supply voltage problems (even though the esp32-cam is sold bundled with the ov5640 which overheats and doesn’t work).

Can someone suggest a somewhat low-priced and low-power solution, using any microprocessor and camera combo? It also needs to be small, smaller than a raspi.

I’ve discovered that the ov5640 starts up fast, under one second with hi-res. But I can’t find any for sale that aren’t wide-angle and on short 28mm cable. Oh well …