It's slow haha. Faster on the Pi Zero 2 with bookworm. I think it's 20-30 seconds.
I use systemd to run main.py let me time it real quick.
Edit: I was off, it's 40 seconds when the intro animation starts playing.
This is why the camera spends most of its time in the home screen state until you're ready to take a photo which is when the live pass through plays or while recording a video (allows you to change focus/aperture while filming). That also conserves power since it has the highest current draw while recording/showing a live preview.
I would advise against running Alpine on a Raspberry Pi (Zero)
Alpine is great for servers or Docker containers, but once you start installing it on barely supported hardware you'll notice the pain.
https://medium.com/@jdc-cunningham/making-a-user-interface-f...
A lot of pictures and full menu map
And MS paint wiring diagrams
(1st camera) https://github.com/jdc-cunningham/pi-zero-hq-cam/tree/master...
(2nd camera orange) https://github.com/jdc-cunningham/modular-pi-cam/blob/master...